Recent zbMATH articles in MSC 62G https://www.zbmath.org/atom/cc/62G 2021-11-25T18:46:10.358925Z Werkzeug Books review of: P. Müller et al., Bayesian nonparametric data analysis https://www.zbmath.org/1472.00009 2021-11-25T18:46:10.358925Z "Bouza, C. N." https://www.zbmath.org/authors/?q=ai:bouza-herrera.carlos-narciso Review of [Zbl 1333.62003]. Convergence in mean and central limit theorems for weighted sums of martingale difference random vectors with infinite $$r$$th moments https://www.zbmath.org/1472.60042 2021-11-25T18:46:10.358925Z "Dung, L. V." https://www.zbmath.org/authors/?q=ai:dung.le-viet "Son, T. C." https://www.zbmath.org/authors/?q=ai:son.tran-cao|son.ta-cong "Tu, T. T." https://www.zbmath.org/authors/?q=ai:tu.teng-tao|tu.ton-that Summary: Let $$(X_{nj};1\leq j\leq m_n,n\geq 1)$$ be an array of rowwise $$\mathbb{R}^d$$-valued martingale difference $$(d\geq 1)$$ with respect to $$\sigma$$-fields $$(\mathcal{F}_{nj};0\leq j\leq m_n,n\geq 1)$$ and let $$(C_{nj};1\leq j\leq m_n,n\geq 1)$$ be an array of $$m\times d$$ matrices of real numbers, where $$(m_n;n\geq 1)$$ is a sequence of positive integers such that $$m_n\rightarrow\infty$$ as $$n\rightarrow\infty$$. The aim of this paper is to establish convergence in mean and central limit theorems for weighted sums type $$S_n=\sum_{j=1}^{m_n}C_{nj}X_{nj}$$ under some conditions of slow variation at infinity. We also apply the obtained results to study the asymptotic properties of estimates in some statistical models. In addition, two illustrative examples and their simulation are given. This study is motivated by models arising in economics, telecommunications, hydrology, and physics applications where the innovations are often dependent on each other and have infinite variances. Conjunction probability of smooth centered Gaussian processes https://www.zbmath.org/1472.60067 2021-11-25T18:46:10.358925Z "Viet-Hung Pham" https://www.zbmath.org/authors/?q=ai:viet-hung-pham. Summary: In this paper we provide an upper bound for the conjunction probability of independent Gaussian smooth processes, and then, we prove that this bound is a good approximation with exponentially smaller error. Our result confirms the heuristic approximation by Euler characteristic method of \textit{K. J. Worsley} and \textit{K. J. Friston} [Stat. Probab. Lett. 47, No. 2, 135--140 (2000; Zbl 0979.62077)] and also implies the exact value of generalized Pickands constant in a special case. Some results for conjunction probability of correlated processes are also discussed. Nonparametric estimation of jump rates for a specific class of piecewise deterministic Markov processes https://www.zbmath.org/1472.60115 2021-11-25T18:46:10.358925Z "Krell, Nathalie" https://www.zbmath.org/authors/?q=ai:krell.nathalie "Schmisser, Émeline" https://www.zbmath.org/authors/?q=ai:schmisser.emeline Summary: In this paper, we consider a unidimensional piecewise deterministic Markov process (PDMP), with homogeneous jump rate $$\lambda (x)$$. This process is observed continuously, so the flow $$\phi$$ is known. To estimate nonparametrically the jump rate, we first construct an adaptive estimator of the stationary density, then we derive a quotient estimator $$\hat{\lambda}_n$$ of $$\lambda$$. Under some ergodicity conditions, we bound the risk of these estimators (and give a uniform bound on a small class of functions), and prove that the estimator of the jump rate is nearly minimax (up to a $$\ln^2(n)$$ factor). The simulations illustrate our theoretical results. Minimax rates in sparse, high-dimensional change point detection https://www.zbmath.org/1472.62013 2021-11-25T18:46:10.358925Z "Liu, Haoyang" https://www.zbmath.org/authors/?q=ai:liu.haoyang "Gao, Chao" https://www.zbmath.org/authors/?q=ai:gao.chao "Samworth, Richard J." https://www.zbmath.org/authors/?q=ai:samworth.richard-j The aim of this paper to study the detection of a sparse change in a high-dimensional mean vector as a minimax testing problem. It means that the authors consider for some $$n\geq 2$$ a $$p\times n$$ matrix $$X$$ that can be written as $X = \theta +E,$ where $$\theta\in \mathbb{R}^{p\times n}$$ is deterministic and the entries of $$E$$ are independent $$N(0, 1)$$ random variables. Their first main contribution is to derive the exact minimax testing rate across all parameter regimes for $$n$$ independent, $$p$$-variate Gaussian observations. The second contribution is that, in a dense asymptotic regime, the authors identify the sharp leading constant. Safe adaptive importance sampling: a mixture approach https://www.zbmath.org/1472.62016 2021-11-25T18:46:10.358925Z "Delyon, Bernard" https://www.zbmath.org/authors/?q=ai:delyon.bernard "Portier, François" https://www.zbmath.org/authors/?q=ai:portier.francois Adaptive importance sampling (AIS) constitutes new samples, such as particles in statistical physics, generated under certain probability distribution called policy $$q_k$$ and the next policy $$q_{k+1}$$ uses the new particles adaptively. In the earlier works, the policy is chosen as the kernel density estimate based on the previous particles reweighted by their importance weights. The authors propose a new approach called safe adaptive importance sampling' (SAIS) which estimates the policy as a mixture of kernel density estimate and certain safe' density with heavier tails. They also consider the functional approximation and derive convergence rates, leading to a central limit theorem for the estimates. It is observed that the asymptotic variance with this procedure is the same as that of an oracle' procedure. Further, a subsampling approach can be adopted to reduce the computational time involved without loosing the original efficiency. A simulation study at the end illustrates the practical nature of the algorithms developed. A section at the end gives detailed mathematical proofs including two appendices. There is a rich list of useful references. Median-unbiasedness and the Gauss-Markov property in finite population survey sampling https://www.zbmath.org/1472.62018 2021-11-25T18:46:10.358925Z "Hedayat, A. S." https://www.zbmath.org/authors/?q=ai:hedayat.abdossamad "Pajda-De La O, Jennifer" https://www.zbmath.org/authors/?q=ai:pajda-de-la-o.jennifer Summary: In this paper, we identify and characterize a family of sampling designs such that, under these designs, the sample median is a median-unbiased estimator of the population median. We first consider the simple random sampling case. A simple random sampling design has the median-unbiasedness property. Moreover, upon deleting samples from the simple random sampling case and imposing a uniform probability distribution on the remaining samples, the sample median is a median-unbiased estimator provided that the support meets a minimum threshold. However, there are other sampling designs, such as those based on balanced incomplete block designs, that do not need to meet the minimum threshold requirement to have the sample median be a median-unbiased estimator. We construct non-uniformly distributed sampling designs that have the median-unbiasedness property as well. In fact, the sample median is a best linear unbiased estimator within the class of linear median unbiased estimators. We show the sample median follows the Gauss-Markov Property under a simple random sampling design. Design-unbiased statistical learning in survey sampling https://www.zbmath.org/1472.62021 2021-11-25T18:46:10.358925Z "Sande, Luis Sanguiao" https://www.zbmath.org/authors/?q=ai:sande.luis-sanguiao "Zhang, Li-Chun" https://www.zbmath.org/authors/?q=ai:zhang.lichun Summary: Design-consistent model-assisted estimation has become the standard practice in survey sampling. However, design consistency remains to be established for many machine-learning techniques that can potentially be very powerful assisting models. We propose a subsampling Rao-Blackwell method, and develop a statistical learning theory for \textit{exactly} design-unbiased estimation with the help of linear or non-linear prediction models. Our approach makes use of classic ideas from Statistical Science as well as the rapidly growing field of Machine Learning. Provided rich auxiliary information, it can yield considerable efficiency gains over standard linear model-assisted methods, while ensuring valid estimation for the given target population, which is robust against potential mis-specifications of the assisting model, even if the design consistency of following the standard recipe for plug-in model-assisted estimator cannot be established. Average treatment effects in the presence of unknown interference https://www.zbmath.org/1472.62022 2021-11-25T18:46:10.358925Z "Sävje, Fredrik" https://www.zbmath.org/authors/?q=ai:savje.fredrik "Aronow, Peter M." https://www.zbmath.org/authors/?q=ai:aronow.peter-m "Hudgens, Michael G." https://www.zbmath.org/authors/?q=ai:hudgens.michael-g It is noted that causal inference usually assumes the absence of interference among the units of the population. However, in certain situations ,especially in social and medical fields, interference is inevitable. In such cases, it is possible to allow moderate amounts of interference in an unknown and arbitrary way. A sample of units is selected and a random subset is assigned to a particular treatment. Here the parameter of interest is the average effect of the assignments under spill over effects. The authors investigate the expected average treatment effect (EATE). They obtain consistent estimates of EATE as well as their variance estimates using Horvitz-Thompson and Ha'jek estimators. Furthermore, they show that EATE for a given experiment is informative of the effect under the designs that are close to the implemented design. Thus external validity is established with a proper definition of measure of closeness, which is an important practical aspect. There is a simulation study in one of the three supplements provided at the end of the paper. Uniform almost sure convergence and asymptotic distribution of the wavelet-based estimators of partial derivatives of multivariate density function under weak dependence https://www.zbmath.org/1472.62031 2021-11-25T18:46:10.358925Z "Allaoui, Soumaya" https://www.zbmath.org/authors/?q=ai:allaoui.soumaya "Bouzebda, Salim" https://www.zbmath.org/authors/?q=ai:bouzebda.salim "Chesneau, Christophe" https://www.zbmath.org/authors/?q=ai:chesneau.christophe "Liu, Jicheng" https://www.zbmath.org/authors/?q=ai:liu.jicheng Summary: This paper is devoted to the estimation of partial derivatives of multivariate density functions. In this regard, nonparametric linear wavelet-based estimators are introduced, showing their attractive properties from the theoretical point of view. In particular, we prove the strong uniform consistency properties of these estimators, over compact subsets of $$\mathbb{R}^d$$, with the determination of the corresponding convergence rates. Then, we establish the asymptotic normality of these estimators. As a main contribution, we relax some standard dependence conditions; our results hold under a weak dependence condition allowing the consideration of mixing, association, Gaussian sequences and Bernoulli shifts. Estimating multi-index models with response-conditional least squares https://www.zbmath.org/1472.62043 2021-11-25T18:46:10.358925Z "Klock, Timo" https://www.zbmath.org/authors/?q=ai:klock.timo "Lanteri, Alessandro" https://www.zbmath.org/authors/?q=ai:lanteri.alessandro "Vigogna, Stefano" https://www.zbmath.org/authors/?q=ai:vigogna.stefano In the general area of sufficient dimension reduction, a novel methodology is derived and analyzed for estimation of the index space $$A$$ of a high dimensional multi-index regression model $$E(Y|X) = g(A^T X)$$ with $$g$$ being a link function. The estimation method is based on the solution of localized least squares problems and uses the span of linear regression slope coefficients computed over level sets of the data. The propagation error of the index space estimate in the regression of the link function is studied in detail. The proposed method is shown to be attractive to practitioners by being computationally efficient and easy to implement as only one hyperparameter (the number of level sets) needs to be specified. Furthermore, finite sample generalization bounds for the regression model are provided which account for the projection error; in turn the bounds are used in quantifying the generalization bound for derived regression estimate and obtain that when response-conditional least squares are paired with piecewise polynomial regression, this leads to optimal estimation of the multi-index model. Causal inference on discrete data via estimating distance correlations https://www.zbmath.org/1472.62044 2021-11-25T18:46:10.358925Z "Liu, Furui" https://www.zbmath.org/authors/?q=ai:liu.furui "Chan, Laiwan" https://www.zbmath.org/authors/?q=ai:chan.laiwan Summary: In this article, we deal with the problem of inferring causal directions when the data are on discrete domain. By considering the distribution of the cause $$P(X)$$ and the conditional distribution mapping cause to effect $$P(Y|X)$$ as independent random variables, we propose to infer the causal direction by comparing the distance correlation between $$P(X)$$ and $$P(Y|X)$$ with the distance correlation between $$P(Y)$$ and $$P(X|Y)$$. We infer that $$X$$ causes $$Y$$ if the dependence coefficient between $$P(X)$$ and $$P(Y|X)$$ is smaller. Experiments are performed to show the performance of the proposed method. Weighted rank estimation of nonparametric transformation models with case-1 and case-2 interval-censored failure time data https://www.zbmath.org/1472.62045 2021-11-25T18:46:10.358925Z "Liu, Tianqing" https://www.zbmath.org/authors/?q=ai:liu.tianqing "Yuan, Xiaohui" https://www.zbmath.org/authors/?q=ai:yuan.xiaohui "Sun, Jianguo" https://www.zbmath.org/authors/?q=ai:sun.jianguo.1|sun.jianguo.2|sun.jianguo Summary: Case-1 and case-2 interval-censored failure time data commonly occur in medical research as well as other fields and many methods have been developed for their analysis under different frameworks. In this paper, we consider regression analysis of such data and present a general class of nonparametric transformation models. One major advantage of these models is their flexibility and generality as they include the linear transformation model as a special case. For estimation of regression parameters, we propose a weighted rank (WR) estimation procedure and establish the consistency and asymptotic normality of the resulting estimator. Furthermore, to estimate the asymptotic covariance matrix of the proposed estimator, a resampling technique, which does not involve nonparametric density estimation or numerical derivatives, is developed. A numerical study is also conducted and suggests that the proposed methodology works well in practice. Finally an application is provided. Consistent regression using data-dependent coverings https://www.zbmath.org/1472.62046 2021-11-25T18:46:10.358925Z "Margot, Vincent" https://www.zbmath.org/authors/?q=ai:margot.vincent "Baudry, Jean-Patrick" https://www.zbmath.org/authors/?q=ai:baudry.jean-patrick "Guilloux, Frederic" https://www.zbmath.org/authors/?q=ai:guilloux.frederic "Wintenberger, Olivier" https://www.zbmath.org/authors/?q=ai:wintenberger.olivier Summary: We introduce a procedure to generate an estimator of the regression function based on a \textit{data-dependent quasi-covering} of the feature space. A quasi-partition is generated from the quasi-covering and the estimator predicts the conditional empirical expectation over the cells of the quasi-partition. We provide sufficient conditions to ensure the consistency of the estimator. Each element of the quasi-covering is labeled as \textit{significant} or \textit{insignificant}. We avoid the condition of cell shrinkage commonly found in the literature for data-dependent partitioning estimators. This reduces the number of elements in the quasi-covering. An important feature of our estimator is that it is \textit{interpretable}. The proof of the consistency is based on a control of the convergence rate of the empirical estimation of conditional expectations, which is interesting in itself. Nonparametric estimation of the conditional distribution function for surrogate data by the regression model https://www.zbmath.org/1472.62047 2021-11-25T18:46:10.358925Z "Metmous, Imane" https://www.zbmath.org/authors/?q=ai:metmous.imane "Attouch, Mohammed Kadi" https://www.zbmath.org/authors/?q=ai:attouch.mohammed-kadi "Mechab, Boubaker" https://www.zbmath.org/authors/?q=ai:mechab.boubaker "Merouan, Torkia" https://www.zbmath.org/authors/?q=ai:merouan.torkia Summary: The main objective of this paper is to estimate the conditional cumulative distribution using the nonparametric kernel method for a surrogated scalar response variable given a functional random one. We introduce the new kernel type estimator for the conditional cumulative distribution function (\textit{cond-cdf}) of this kind of data. Afterward, we estimate the quantile by inverting this estimated \textit{cond-cdf} and state the asymptotic properties. The uniform almost complete convergence (with rate) of the kernel estimate of this model and the quantile estimator is established. Finally, a simulation study completed to show how our methodology can be adopted. The law of the iterated logarithm and maximal smoothing principle for the kernel distribution function estimator https://www.zbmath.org/1472.62048 2021-11-25T18:46:10.358925Z "Swanepoel, Jan W. H." https://www.zbmath.org/authors/?q=ai:swanepoel.jan-w-h Summary: Two new properties of the kernel distribution function estimator of diverse nature are derived. Firstly, a law of the iterated logarithm is proved for both the integrated absolute error and the integrated squared error of the estimator. Secondly, the maximal smoothing principle in kernel density estimation developed by Terrell is extended to kernel distribution function estimation, which allows, among others, the derivation of an alternative quick-and-simple bandwidth selector. In fact, there is a common link between the two topics: both problems are solved through the use of the same, not-so-standard, methodology. The results based on simulated data and a real data set are also presented. Weighted geometric mean and its properties https://www.zbmath.org/1472.62049 2021-11-25T18:46:10.358925Z "Turchyn, Ievgen" https://www.zbmath.org/authors/?q=ai:turchyn.ievgen Summary: Various means (the arithmetic mean, the geometric mean, the harmonic mean, the power means) are often used as central tendency statistics. A new statistic of such type is offered for a sample from a distribution on the positive semi-axis, the $$\gamma$$-weighted geometric mean. This statistic is a certain weighted geometric mean with adaptive weights. Monte Carlo simulations showed that the $$\gamma$$-weighted geometric mean possesses low variance: smaller than the variance of the 0.20-trimmed mean for the Lomax distribution. The bias of the new statistic was also studied. We studied the bias in terms of nonparametric confidence intervals for the quantiles which correspond of our statistic for the case of the Lomax distribution. Deviation from the median for the $$\gamma$$-weighted geometric mean was measured in terms of the MSE for the log-logistic distribution and the Nakagami distribution (the MSE for the $$\gamma$$-weighted geometric mean was comparable or smaller than the MSE for the sample median). Estimation of shape constrained additive models with missing response at random https://www.zbmath.org/1472.62050 2021-11-25T18:46:10.358925Z "Wang, Lu" https://www.zbmath.org/authors/?q=ai:wang.lu.3|wang.lu.1|wang.lu.2|wang.lu.4|wang.lu "Zhou, Xiao-Hua" https://www.zbmath.org/authors/?q=ai:zhou.xiao-hua-andrew Summary: Shape constrained additive models are useful in estimating production functions or analysing disease risk where the relationship between predictors and response is known to be monotone or/and concave. We here consider the estimation of shape constrained additive models when the response is missing at random given missing data are common occurrence and problem in many real-life situations. To the best of our knowledge, no research has focused on this problem. Our paper nicely fills this gap and contributes to the literature by proposing a weighted constrained polynomial spline estimation method in a one-step backfitting procedure. The proposed method is not only easy to implement but also gives smooth estimators that satisfy shape constraints and accommodate missing data problem simultaneously. In theory, we show that the proposed estimator enjoys the optimal rate of convergence asymptotically. Both simulation studies and the application of our method to Norwegian farm data illustrate that the proposed method has superior performance due to the incorporation of weights and shape constraints. Weighted empirical likelihood inferences for a class of varying coefficient ARCH-M models https://www.zbmath.org/1472.62051 2021-11-25T18:46:10.358925Z "Zhao, Peixin" https://www.zbmath.org/authors/?q=ai:zhao.peixin "Yang, Yiping" https://www.zbmath.org/authors/?q=ai:yang.yiping "Zhou, Xiaoshuang" https://www.zbmath.org/authors/?q=ai:zhou.xiaoshuang Summary: In this paper, we consider the empirical likelihood inferences for a class of varying coefficient ARCH-M models, which is an extended version of parametric ARCH-M models. By constructing a weighted auxiliary random vector, we propose a weighted empirical likelihood method for estimating the functional-coefficients. Under some regularity conditions, the constructed empirical log-likelihood ratio is shown to be asymptotically $$\chi^2$$, and then the pointwise confidence interval for functional-coefficient is constructed. Some simulation studies are carried out to compare finite sample performances of the proposed empirical likelihood estimation method with some existing estimation methods under various model settings. A real data analysis is also undertaken to illustrate practical implementation and performance of the proposed estimation procedure. Efficient estimation in heteroscedastic single-index models https://www.zbmath.org/1472.62052 2021-11-25T18:46:10.358925Z "Zhao, Yan-Yong" https://www.zbmath.org/authors/?q=ai:zhao.yanyong "Li, Jianquan" https://www.zbmath.org/authors/?q=ai:li.jianquan "Wang, Hong-Xia" https://www.zbmath.org/authors/?q=ai:wang.hongxia "Zhao, Honghong" https://www.zbmath.org/authors/?q=ai:zhao.honghong "Chen, Xueping" https://www.zbmath.org/authors/?q=ai:chen.xueping Summary: In this article, we focus on the efficient estimation in single-index models with heteroscedastic errors. We first develop a nonparametric estimator of the variance function based on a fully nonparametric function or a dimension reduction structure, and the resulting estimator is consistent. Then, we propose a reweighting estimator of the parametric component via taking the estimated variance function into account, and the main results show that it has a smaller asymptotic variance than the naive estimator that neglects the heteroscedasticity. Simulation studies are conducted to evaluate the efficacy of the proposed methodologies, and an analysis of a real data example is provided for illustration. On some smooth estimators of the quantile function for a stationary associated process https://www.zbmath.org/1472.62053 2021-11-25T18:46:10.358925Z "Chaubey, Yogendra P." https://www.zbmath.org/authors/?q=ai:chaubey.yogendra-p "Dewan, Isha" https://www.zbmath.org/authors/?q=ai:dewan.isha "Li, Jun" https://www.zbmath.org/authors/?q=ai:li.jun.8|li.jun.1|li.jun.3|li.jun|li.jun.14|li.jun.10|li.jun.6|li.jun.13|li.jun.11|li.jun.12|li.jun.2|li.jun.7 The authors aimed to quantile function estimation to estimating marginal distribution function. Various estimators in this class of estimators are contrasted, through a simulation study, among themselves and with an indirect smooth quantile estimator obtained by inverting the Poisson weights based estimator of the distribution function studied in [\textit{Y. P. Chaubey} et al., Stat. Probab. Lett. 81, No. 2, 267--276 (2011; Zbl 1270.62067)]. The indirect smoothing estimator seems to be the best estimator on account of smaller MSE, however, a quantile estimator based on the Bernstein polynomials and that using the corrected Poisson weights turn out to be almost as good as the inverse distribution function estimator using Poisson weights. As far as my knowledge goes, the author's statistical approach fulfills the standards of the journal. The abstract is succinct and appropriate and reflecting the essence of the paper. The methodology used is clear and utmost care is taken about typographical errors. It seems that the authors explained an important conclusion based on the numerical studies is that the quantile estimator obtained by inverting the smooth estimator of the distribution function using Poisson weights comes out to be the best amongst the considered estimators. On the other hand, the direct smooth estimators using the normalized Poisson weights and Bernstein polynomials are good competitors. The authors explained through theoretically. Density deconvolution with non-standard error distributions: rates of convergence and adaptive estimation https://www.zbmath.org/1472.62054 2021-11-25T18:46:10.358925Z "Goldenshluger, Alexander" https://www.zbmath.org/authors/?q=ai:goldenshluger.alexander "Kim, Taeho" https://www.zbmath.org/authors/?q=ai:kim.taeho Summary: It is a standard assumption in the density deconvolution problem that the characteristic function of the measurement error distribution is non-zero on the real line. While this condition is assumed in the majority of existing works on the topic, there are many problem instances of interest where it is violated. In this paper we focus on non-standard settings where the characteristic function of the measurement errors has zeros, and study how zeros multiplicity affects the estimation accuracy. For a prototypical problem of this type we demonstrate that the best achievable estimation accuracy is determined by the multiplicity of zeros, the rate of decay of the error characteristic function, as well as by the smoothness and the tail behavior of the estimated density. We derive lower bounds on the minimax risk and develop optimal in the minimax sense estimators. In addition, we consider the problem of adaptive estimation and propose a data-driven estimator that automatically adapts to unknown smoothness and tail behavior of the density to be estimated. Recursive asymmetric kernel density estimation for nonnegative data https://www.zbmath.org/1472.62055 2021-11-25T18:46:10.358925Z "Kakizawa, Yoshihide" https://www.zbmath.org/authors/?q=ai:kakizawa.yoshihide Summary: Recursive nonparametric density estimation for nonnegative data is considered, using an asymmetric kernel with nonnegative support. It has a computational advantage in a situation where a huge number of data are sequentially collected. The recursive asymmetric kernel estimator keeps desirable asymptotic properties similar to the ordinary non-recursive asymmetric kernel estimator. Also, simulation studies and a real data analysis are performed for illustration. Spectral cut-off regularisation for density estimation under multiplicative measurement errors https://www.zbmath.org/1472.62056 2021-11-25T18:46:10.358925Z "Miguel, Sergio Brenner" https://www.zbmath.org/authors/?q=ai:miguel.sergio-brenner "Comte, Fabienne" https://www.zbmath.org/authors/?q=ai:comte.fabienne "Johannes, Jan" https://www.zbmath.org/authors/?q=ai:johannes.jan Summary: We study the non-parametric estimation of an unknown density $$f$$ with support on $$\mathbb{R}_+$$ based on an i.i.d. sample with multiplicative measurement errors. The proposed fully-data driven procedure is based on the estimation of the Mellin transform of the density $$f$$, a regularisation of the inverse of the Mellin transform by a spectral cut-off and a data-driven model selection in order to deal with the upcoming bias-variance trade-off. We introduce and discuss further \textit{Mellin-Sobolev spaces} which characterize the regularity of the unknown density $$f$$ through the decay of its Mellin transform. Additionally, we show minimax-optimality over \textit{Mellin-Sobolev spaces} of the data-driven density estimator and hence its adaptivity. Minimax bounds for Besov classes in density estimation https://www.zbmath.org/1472.62057 2021-11-25T18:46:10.358925Z "Sart, Mathieu" https://www.zbmath.org/authors/?q=ai:sart.mathieu Summary: We study the problem of density estimation on $$[0,1]$$ under $$\mathbb{L}^p$$ norm. We carry out a new piecewise polynomial estimator and prove that it is simultaneously (near)-minimax over a very wide range of Besov classes $$\mathcal{B}_{\pi,\infty}^\alpha(R)$$. In particular, we may deal with unbounded densities and shed light on the minimax rates of convergence when $$\pi < p$$ and $$\alpha \in (1/ \pi -1/ p,1/ \pi]$$. Erratum to: `Estimation and uncertainty quantification for extreme quantile regions'' https://www.zbmath.org/1472.62058 2021-11-25T18:46:10.358925Z "Beranger, Boris" https://www.zbmath.org/authors/?q=ai:beranger.boris "Padoan, Simone A." https://www.zbmath.org/authors/?q=ai:padoan.simone-a "Sisson, Scott A." https://www.zbmath.org/authors/?q=ai:sisson.scott-a Erratum to the authors' paper [ibid. 24, No. 2, 349--375 (2021; Zbl 1466.62291)]. Nonparametric relative error estimation via functional regressor by the $$k$$ nearest neighbors smoothing under truncation random data https://www.zbmath.org/1472.62059 2021-11-25T18:46:10.358925Z "Bouabsa, Wahiba" https://www.zbmath.org/authors/?q=ai:bouabsa.wahiba Summary: The relation between a functional random covariate and a scalar answer due to left truncation by a different random variable is evaluated in this study with the kNN method. In particular, in order to produce a nonparametric kNN regression operator of these functional truncated data as a loss function, we should use mean squared relative error. In number of neighbors, we establish an estimator and assess the uniform consistency performance with the convergence rate. Then, for different levels of computational truncated data, a simulation analysis was carried out on finite-sized samples to show the feasibility of our estimation procedure and to highlight its superiority to traditional kernel estimation. A distributed quantile estimation algorithm of heavy-tailed distribution with massive datasets https://www.zbmath.org/1472.62060 2021-11-25T18:46:10.358925Z "Xie, Xiaoyue" https://www.zbmath.org/authors/?q=ai:xie.xiaoyue "Shi, Jian" https://www.zbmath.org/authors/?q=ai:shi.jian Summary: Quantile estimation with big data is still a challenging problem in statistics. In this paper we introduce a distributed algorithm for estimating high quantiles of heavy-tailed distributions with massive datasets. The key idea of the algorithm is to apply the alternating direction method of multipliers in parameter estimation of the generalized pareto distribution in a distributed structure and compute high quantiles based on parameter estimation by the Peak Over Threshold method. This paper proves that the proposed algorithm converges to a stationary solution when the step size is properly chosen. The numerical study and real data analysis also shows that the algorithm is feasible and efficient for estimating high quantiles of heavy-tailed distribution with massive datasets and there is a clear-cut winner for the extreme quantiles. Multivariate variable selection by means of null-beamforming https://www.zbmath.org/1472.62061 2021-11-25T18:46:10.358925Z "Zhang, Jian" https://www.zbmath.org/authors/?q=ai:zhang.jian|zhang.jian.6|zhang.jian.3|zhang.jian.5|zhang.jian.2|zhang.jian.7|zhang.jian.1|zhang.jian.4 "Oftadeh, Elaheh" https://www.zbmath.org/authors/?q=ai:oftadeh.elaheh Summary: This article aims to use beamforming, a covariate-assisted data projection method to solve the problem of variable selection for multivariate random-effects regression models. The new approach attempts to explore the covariance structure in the data with a small number of random-effects covariates. The basic premise behind the proposal is to scan through a covariate space with a series of forward filters named null-beamformers; each is tailored to a particular covariate in the space and resistant to interference effects originating from other covariates. Applying the proposed method to simulated and real multivariate regression data, we show that it can substantially outperform the existing methods of multivariate variable selection in terms of sensitivity and specificity. A theory on selection consistency is established under certain regularity conditions. Composite empirical likelihood for multisample clustered data https://www.zbmath.org/1472.62062 2021-11-25T18:46:10.358925Z "Chen, Jiahua" https://www.zbmath.org/authors/?q=ai:chen.jiahua "Li, Pengfei" https://www.zbmath.org/authors/?q=ai:li.pengfei "Liu, Yukun" https://www.zbmath.org/authors/?q=ai:liu.yukun "Zidek, James V." https://www.zbmath.org/authors/?q=ai:zidek.james-v Summary: In many applications, data cluster. Failing to take the cluster structure into consideration generally leads to underestimated variances of point estimators and inflated type I errors in hypothesis tests. Many circumstance-dependent approaches have been developed to handle clustered data. A working covariance matrix may be used in generalised estimating equations. One may throw out the cluster structure and use only the cluster means, or explicitly model the cluster structure. Our interest is the case where multiple samples of clustered data are collected, and the population quantiles are particularly important. We develop a composite empirical likelihood for clustered data under a density ratio model. This approach avoids parametric assumptions on the population distributions or the cluster structure. It efficiently utilises the common features of the multiple populations and the exchangeability of the cluster members. We also develop a cluster-based bootstrap method to provide valid variance estimation and to control the type I errors. We examine the performance of the proposed method through simulation experiments and illustrate its usage via a real-world example. Model-based bootstrap for detection of regional quantile treatment effects https://www.zbmath.org/1472.62063 2021-11-25T18:46:10.358925Z "Sun, Yuan" https://www.zbmath.org/authors/?q=ai:sun.yuan "He, Xuming" https://www.zbmath.org/authors/?q=ai:he.xuming Summary: Quantile treatment effects are often considered in a quantile regression framework to adjust for the effect of covariates. In this study, we focus on the problem of testing whether the treatment effect is significant at a set of quantile levels (e.g. lower quantiles). We propose a regional quantile regression rank test as a generalisation of the rank test at an individual quantile level. This test statistic allows us to detect the treatment effect for a prespecified quantile interval by integrating the regression rank scores over the region of interest. A new model-based bootstrap method is constructed to estimate the null distribution of the test statistic. A simulation study is conducted to demonstrate the validity and usefulness of the proposed test. We also demonstrate the use of the proposed method through an analysis of the 2016 US birth weight data and selected S\&P 500 sector portfolio data. An inverse norm weight spatial sign test for high-dimensional directional data https://www.zbmath.org/1472.62064 2021-11-25T18:46:10.358925Z "Wang, Hongfei" https://www.zbmath.org/authors/?q=ai:wang.hongfei "Feng, Long" https://www.zbmath.org/authors/?q=ai:feng.long "Liu, Binghui" https://www.zbmath.org/authors/?q=ai:liu.binghui "Zhou, Qin" https://www.zbmath.org/authors/?q=ai:zhou.qin Summary: In this paper, we focus on the high-dimensional location testing problem of directional data under the assumption of rotationally symmetric distributions, where the data dimension is potentially much larger than the sample size. We study the family of directional weighted spatial sign tests for this testing problem and establish the asymptotic null distributions and local power properties of this family. In particular, we find that the test based on the inverse norm weight, named as the inverse norm weight spatial sign test, has the maximum asymptotic power in this family. As demonstrated by extensive numerical results, the inverse norm weight spatial sign test has advantages in empirical power compared with some other members in the family as well as some existing tests. Some asymptotic properties of conditional density function for functional data under random censorship https://www.zbmath.org/1472.62065 2021-11-25T18:46:10.358925Z "Akkal, Fatima" https://www.zbmath.org/authors/?q=ai:akkal.fatima "Rabhi, Abbes" https://www.zbmath.org/authors/?q=ai:rabhi.abbes "Keddani, Latifa" https://www.zbmath.org/authors/?q=ai:keddani.latifa Summary: In this work, we investigate the asymptotic properties of a nonparametric mode of a conditional density when the real response variable is censored and the explanatory variable is valued in a semi-metric space under ergodic data. First of all, we establish asymptotic properties for a conditional density estimator from which we derive an central limit theorem (CLT) of the conditional mode estimator. Simulation study is also presented to illustrate the validity and finite sample performance of the considered estimator. A modified discrepancy principle to attain optimal convergence rates under unknown noise https://www.zbmath.org/1472.62066 2021-11-25T18:46:10.358925Z "Jahn, Tim" https://www.zbmath.org/authors/?q=ai:jahn.tim On the uniform-in-bandwidth consistency of the general conditional $$U$$-statistics based on the copula representation https://www.zbmath.org/1472.62067 2021-11-25T18:46:10.358925Z "Bouzebda, Salim" https://www.zbmath.org/authors/?q=ai:bouzebda.salim "Elhattab, Issam" https://www.zbmath.org/authors/?q=ai:elhattab.issam "Nemouchi, Boutheina" https://www.zbmath.org/authors/?q=ai:nemouchi.boutheina Summary: \textit{W. Stute} [Ann. Probab. 19, No. 2, 812--825 (1991; Zbl 0770.60035)] introduced a class of estimators called conditional $$U$$-statistics of $\mathbb{E} (\varphi (Y_1 , \ldots , Y_m ) \, | \, (X_1 , \ldots , X_m ) = \mathbf{t} ), \quad \text{for } \mathbf{t} \in \mathbb{R}^m .$ In the present work, we provide a new class of estimators of conditional $$U$$-statistics. More precisely, we investigate the conditional $$U$$-statistics based on copula representation. We establish the uniform-in-bandwidth consistency for the proposed estimator. Our theorems allow data-driven local bandwidths for these statistics. The theoretical uniform consistency results, established in this paper, are (or will be) key tools for many further developments in copula regression analysis. The performance of these procedures is evaluated through simulation in the context of the conditional Kendall's tau. Wavelet-based Benjamini-Hochberg procedures for multiple testing under dependence https://www.zbmath.org/1472.62068 2021-11-25T18:46:10.358925Z "Ghosh, Debashis" https://www.zbmath.org/authors/?q=ai:ghosh.debashis.1|ghosh.debashis Summary: Multiple comparisons methodology has experienced a resurgence of interest due to the increase in high-dimensional datasets generated from various biological, medical and scientific fields. An outstanding problem in this area is how to perform testing in the presence of dependence between the $$p$$-values. We propose a novel approach to this problem based on a spacings-based representation of the Benjamini-Hochberg procedure. The representation leads to a new application of the wavelet transform to effectively decorrelate $$p$$-values. Theoretical justification for the procedure is shown. The power gains of the proposed methodology relative to existing procedures is demonstrated using both simulated and real datasets. Adaptive estimation in symmetric location model under log-concavity constraint https://www.zbmath.org/1472.62069 2021-11-25T18:46:10.358925Z "Laha, Nilanjana" https://www.zbmath.org/authors/?q=ai:laha.nilanjana Summary: We revisit the problem of estimating the center of symmetry $$\theta$$ of an unknown symmetric density $$f$$. Although \textit{C. J. Stone} [Ann. Stat. 3, 267--284 (1975; Zbl 0303.62026)], \textit{C. van Eeden} [Ann. Math. Stat. 41, 172--181 (1970; Zbl 0218.62043)], and \textit{J. Sacks} [Ann. Stat. 3, 285--298 (1975; Zbl 0329.62032)] constructed adaptive estimators of $$\theta$$ in this model, their estimators depend on external tuning parameters. In an effort to reduce the burden of tuning parameters, we impose an additional restriction of log-concavity on $$f$$. We construct truncated one-step estimators which are adaptive under the log-concavity assumption. Our simulations indicate that the untruncated version of the one step estimator, which is tuning parameter free, is also asymptotically efficient. We also study the maximum likelihood estimator (MLE) of $$\theta$$ in the shape-restricted model. A variance shift model for detection of outliers in the linear measurement error model https://www.zbmath.org/1472.62070 2021-11-25T18:46:10.358925Z "Babadi, Babak" https://www.zbmath.org/authors/?q=ai:babadi.babak "Rasekh, Abdolrahman" https://www.zbmath.org/authors/?q=ai:rasekh.abdolrahman "Rasekhi, Ali Akbar" https://www.zbmath.org/authors/?q=ai:rasekhi.ali-akbar "Zare, Karim" https://www.zbmath.org/authors/?q=ai:zare.karim "Zadkarami, Mohammad Reza" https://www.zbmath.org/authors/?q=ai:zadkarami.mohammad-reza Summary: We present a variance shift model for a linear measurement error model using the corrected likelihood of \textit{T. Nakamura} [Biometrika 77, No. 1, 127--137 (1990; Zbl 0691.62066)]. This model assumes that a single outlier arises from an observation with inflated variance. The corrected likelihood ratio and the score test statistics are proposed to determine whether the $$i$$th observation has an inflated variance. A parametric bootstrap procedure is used to obtain empirical distributions of the test statistics and a simulation study has been used to show the performance of proposed tests. Finally, a real data example is given for illustration. Uncovering causality from multivariate Hawkes integrated cumulants https://www.zbmath.org/1472.62076 2021-11-25T18:46:10.358925Z "Achab, Massil" https://www.zbmath.org/authors/?q=ai:achab.massil "Bacry, Emmanuel" https://www.zbmath.org/authors/?q=ai:bacry.emmanuel "Gaïffas, Stéphane" https://www.zbmath.org/authors/?q=ai:gaiffas.stephane "Mastromatteo, Iacopo" https://www.zbmath.org/authors/?q=ai:mastromatteo.iacopo "Muzy, Jean-François" https://www.zbmath.org/authors/?q=ai:muzy.jean-francois Summary: We design a new nonparametric method that allows one to estimate the matrix of integrated kernels of a multivariate Hawkes process. This matrix not only encodes the mutual influences of each node of the process, but also disentangles the causality relationships between them. Our approach is the first that leads to an estimation of this matrix \textit{without any parametric modeling and estimation of the kernels themselves}. As a consequence, it can give an estimation of causality relationships between nodes (or users), based on their activity timestamps (on a social network for instance), without knowing or estimating the shape of the activities lifetime. For that purpose, we introduce a moment matching method that fits the second-order and the third-order integrated cumulants of the process. A theoretical analysis allows us to prove that this new estimation technique is consistent. Moreover, we show, on numerical experiments, that our approach is indeed very robust with respect to the shape of the kernels and gives appealing results on the MemeTracker database and on financial order book data. Inference problem in generalized fractional Ornstein-Uhlenbeck processes with change-point https://www.zbmath.org/1472.62081 2021-11-25T18:46:10.358925Z "Nkurunziza, Sévérien" https://www.zbmath.org/authors/?q=ai:nkurunziza.severien Summary: In this paper, we study an inference problem in generalized fractional Ornstein-Uhlenbeck (O-U) processes with an unknown change-point when the drift parameter is suspected to satisfy some constraints. The constraint considered is very general and, the testing problem studied generalizes a very recent inference problem in generalized O-U processes. We derive the unrestricted estimator (UE) and the restricted estimator (RE) and we establish the asymptotic properties of the UE and RE. We also propose some shrinkage-type estimators (SEs) as well as a test for testing the constraint. Finally, we derive the asymptotic power of the proposed test and we study the relative risk dominance of the proposed estimators. Modified martingale difference correlations https://www.zbmath.org/1472.62087 2021-11-25T18:46:10.358925Z "Zhou, Jingke" https://www.zbmath.org/authors/?q=ai:zhou.jingke "Zhu, Lixing" https://www.zbmath.org/authors/?q=ai:zhu.lixing Summary: To ameliorate some drawbacks of Martingale Difference Correlation (MDC) such as the asymmetry in the sense that for a pair of vectors, the value of \textit{MDC} may not be equal to 1, and the self-\textit{MDC} of any random vector can be different from vector to vector in value, we in this paper propose a modified MDC (MMDC). Further, as the corresponding partial MDC (PMDC), with controlling another random vector, cannot ensure the equivalence between conditional mean independence and zero PMDC, we then also propose a modified partial MDC (MPMDC) to guarantee, under some regularity conditions, the equivalence. We further investigate the theoretical properties of the corresponding unbiased estimators and apply them to variable screening and hypothesis testing. Numerical studies and real data analysis are conducted to examine their finite sample performances. Cluster validity indices for mixture hazards regression models https://www.zbmath.org/1472.62091 2021-11-25T18:46:10.358925Z "Chang, Yi-Wen" https://www.zbmath.org/authors/?q=ai:chang.yi-wen "Lu, Kang-Ping" https://www.zbmath.org/authors/?q=ai:lu.kang-ping "Chang, Shao-Tung" https://www.zbmath.org/authors/?q=ai:chang.shao-tung Summary: In the analysis of survival data, the problems of competing risks arise frequently in medical applications where individuals fail from multiple causes. Semiparametric mixture regression models have become a prominent approach in competing risks analysis due to their flexibility and easy interpretation of resultant estimates. The literature presents several semiparametric methods on the estimations for mixture Cox proportional hazards models, but fewer works appear on the determination of the number of model components and the estimation of baseline hazard functions using kernel approaches. These two issues are important because both incorrect number of components and inappropriate baseline functions can lead to insufficient estimates of mixture Cox hazard models. This research thus proposes four validity indices to select the optimal number of model components based on the posterior probabilities and residuals resulting from the application of an EM-based algorithm on a mixture Cox regression model. We also introduce a kernel approach to produce a smooth estimate of the baseline hazard function in a mixture model. The effectiveness and the preference of the proposed cluster indices are demonstrated through a simulation study. An analysis on a prostate cancer dataset illustrates the practical use of the proposed method. Linear embedding by joint robust discriminant analysis and inter-class sparsity https://www.zbmath.org/1472.62093 2021-11-25T18:46:10.358925Z "Dornaika, F." https://www.zbmath.org/authors/?q=ai:dornaika.fadi "Khoder, A." https://www.zbmath.org/authors/?q=ai:khoder.a Summary: Linear Discriminant Analysis (LDA) and its variants are widely used as feature extraction methods. They have been used for different classification tasks. However, these methods have some limitations that need to be overcome. The main limitation is that the projection obtained by LDA does not provide a good interpretability for the features. In this paper, we propose a novel supervised method used for multi-class classification that simultaneously performs feature selection and extraction. The targeted projection transformation focuses on the most discriminant original features, and at the same time, makes sure that the transformed features (extracted features) belonging to each class have common sparsity. Our proposed method is called Robust Discriminant Analysis with Feature Selection and Inter-class Sparsity (RDA$$_-$$FSIS). The corresponding model integrates two types of sparsity. The first type is obtained by imposing the $$\ell_{2,1}$$ constraint on the projection matrix in order to perform feature selection. The second type of sparsity is obtained by imposing the inter-class sparsity constraint used for ensuring a common sparsity structure in each class. An orthogonal matrix is also introduced in our model in order to guarantee that the extracted features can retain the main variance of the original data and thus improve the robustness to noise. The proposed method retrieves the LDA transformation by taking into account the two types of sparsity. Various experiments are conducted on several image datasets including faces, objects and digits. The projected features are used for multi-class classification. Obtained results show that the proposed method outperforms other competing methods by learning a more compact and discriminative transformation. On histogram-based regression and classification with incomplete data https://www.zbmath.org/1472.62095 2021-11-25T18:46:10.358925Z "Han, Eric" https://www.zbmath.org/authors/?q=ai:han.eric "Mojirsheibani, Majid" https://www.zbmath.org/authors/?q=ai:mojirsheibani.majid Summary: We consider the problem of nonparametric regression with possibly incomplete covariate vectors. The proposed estimators, which are based on histogram methods, are fully nonparametric and straightforward to implement. The presence of incomplete covariates is handled by an inverse weighting method, where the weights are estimates of the conditional probabilities of having incomplete covariate vectors. We also derive various exponential bounds on the $$L_1$$ norms of our estimators, which can be used to establish strong consistency results for the corresponding, closely related, problem of nonparametric classification with missing covariates. As the main focus and application of our results, we consider the problem of pattern recognition and statistical classification in the presence of incomplete covariates and propose histogram classifiers that are asymptotically optimal. Bayesian sparse linear regression with unknown symmetric error https://www.zbmath.org/1472.62107 2021-11-25T18:46:10.358925Z "Chae, Minwoo" https://www.zbmath.org/authors/?q=ai:chae.minwoo "Lin, Lizhen" https://www.zbmath.org/authors/?q=ai:lin.lizhen "Dunson, David B." https://www.zbmath.org/authors/?q=ai:dunson.david-b Summary: We study Bayesian procedures for sparse linear regression when the unknown error distribution is endowed with a non-parametric prior. Specifically, we put a symmetrized Dirichlet process mixture of Gaussian prior on the error density, where the mixing distributions are compactly supported. For the prior on regression coefficients, a mixture of point masses at zero and continuous distributions is considered. Under the assumption that the model is well specified, we study behavior of the posterior with diverging number of predictors. The compatibility and restricted eigenvalue conditions yield the minimax convergence rate of the regression coefficients in $$\ell_1$$- and $$\ell_2$$-norms, respectively. In addition, strong model selection consistency and a semi-parametric Bernstein-von Mises theorem are proven under slightly stronger conditions. Joint outlier detection and variable selection using discrete optimization https://www.zbmath.org/1472.62110 2021-11-25T18:46:10.358925Z "Jammal, Mahdi" https://www.zbmath.org/authors/?q=ai:jammal.mahdi "Canu, Stephane" https://www.zbmath.org/authors/?q=ai:canu.stephane "Abdallah, Maher" https://www.zbmath.org/authors/?q=ai:abdallah.maher Summary: In regression, the quality of estimators is known to be very sensitive to the presence of spurious variables and outliers. Unfortunately, this is a frequent situation when dealing with real data. To handle outlier proneness and achieve variable selection, we propose a robust method performing the outright rejection of discordant observations together with the selection of relevant variables. A natural way to define the corresponding optimization problem is to use the $$\ell_0$$ norm and recast it as a mixed integer optimization problem. To retrieve this global solution more efficiently, we suggest the use of additional constraints as well as a clever initialization. To this end, an efficient and scalable non-convex proximal alternate algorithm is introduced. An empirical comparison between the $$\ell_0$$ norm approach and its $$\ell_1$$ relaxation is presented as well. Results on both synthetic and real data sets provided that the mixed integer programming approach and its discrete first order warm start provide high quality solutions. Penalised empirical likelihood for semiparametric varying-coefficient partially linear errors-in-variables models https://www.zbmath.org/1472.62114 2021-11-25T18:46:10.358925Z "Yan, Li" https://www.zbmath.org/authors/?q=ai:yan.li "He, Junwei" https://www.zbmath.org/authors/?q=ai:he.junwei "Chen, Xia" https://www.zbmath.org/authors/?q=ai:chen.xia.1 Summary: In this paper, we study the variable selection and parameter estimation for the semiparametric varying-coefficient partially linear models when the covariates are measured with errors. The proposed penalised empirical likelihood estimators are shown to possess the oracle property. Also, we conclude that the asymptotic distribution of penalised empirical likelihood ratio test statistic is a chi-square distribution under the null hypothesis. Some simulations and an application are given to illustrate the performance of the proposed method. Iteratively reweighted $$\ell_1$$-penalized robust regression https://www.zbmath.org/1472.62116 2021-11-25T18:46:10.358925Z "Pan, Xiaoou" https://www.zbmath.org/authors/?q=ai:pan.xiaoou "Sun, Qiang" https://www.zbmath.org/authors/?q=ai:sun.qiang "Zhou, Wen-Xin" https://www.zbmath.org/authors/?q=ai:zhou.wen-xin Summary: This paper investigates tradeoffs among optimization errors, statistical rates of convergence and the effect of heavy-tailed errors for high-dimensional robust regression with nonconvex regularization. When the additive errors in linear models have only bounded second moments, we show that iteratively reweighted $$\ell_1$$-penalized adaptive Huber regression estimator satisfies exponential deviation bounds and oracle properties, including the oracle convergence rate and variable selection consistency, under a weak beta-min condition. Computationally, we need as many as $$\mathcal{O}(\log s+\log \log d)$$ iterations to reach such an oracle estimator, where $$s$$ and $$d$$ denote the sparsity and ambient dimension, respectively. Extension to a general class of robust loss functions is also considered. Numerical studies lend strong support to our methodology and theory. Stochastic comparisons of systems with heterogeneous log-logistic components https://www.zbmath.org/1472.62121 2021-11-25T18:46:10.358925Z "Ghosh, Shyamal" https://www.zbmath.org/authors/?q=ai:ghosh.shyamal "Majumder, Priyanka" https://www.zbmath.org/authors/?q=ai:majumder.priyanka "Mitra, Murari" https://www.zbmath.org/authors/?q=ai:mitra.murari Summary: The log-logistic distribution is a resilient family of life distributions that have been applied in an enormous number of fields. In this paper, we study stochastic comparisons for both parallel and series systems having heterogeneous log-logistic distributed components. The comparisons are performed in the sense of stochastic, reversed hazard rate, hazard rate, and likelihood ratio orderings. The consequences of the changes in the scale parameters or the shape parameters on the magnitude of the smallest and largest order statistics are also investigated in the sense of the above-mentioned orderings. For the entire collection see [Zbl 1466.91004]. Quickest detection of an accumulated state-dependent change point https://www.zbmath.org/1472.62128 2021-11-25T18:46:10.358925Z "Cai, Liang" https://www.zbmath.org/authors/?q=ai:cai.liang The paper deals with change point estimation for continuous-time processes. Using discretization of time, the author reduces the problem to the task of unsettling a Markov process, similar in essence to that considered in the work of \textit{L. Cai} et al. [Sequential Anal. 36, No. 4, 553--562 (2017; Zbl 06840593)] (see also [\textit{W. Sarnowski} and \textit{K. Szajowski}, Stochastics 83, No. 4--6, 569--581 (2011; Zbl 1235.60041)]). The author proposes a model change point detection method dependent on the state of the process, unlike the classical Shiryaev-Roberts procedure (cf. [\textit{A. N. Shiryaev}, Theory Probab. Appl. 8, 22--46 (1963; Zbl 0213.43804); translation from Teor. Veroyatn. Primen. 8, 26--51 (1963)]). State dependence means that the priori probability of the change point depends on the current state. The problem is reduced to finding the optimal stopping time of a vector-valued Markov process. A numerical example illustrates the scheme. Purely sequential FWCI and MRPE problems for the mean of a normal population by sampling in groups with illustrations using breast cancer data https://www.zbmath.org/1472.62130 2021-11-25T18:46:10.358925Z "Mukhopadhyay, Nitis" https://www.zbmath.org/authors/?q=ai:mukhopadhyay.nitis "Wang, Zhe" https://www.zbmath.org/authors/?q=ai:wang.zhe In the paper the authors afresh two fundamental problems on sequential estimation: (i) the fixedwidth confidence interval (FWCI) estimation problem and (ii) the minimum risk point estimation (MRPE) problem, both in the context of estimating an unknown mean $$\mu$$ in an $$\text{N}(\mu,\sigma^2)$$ population where $$\sigma^2$$ is also assumed unknown. The article continues the discussion of FWCI ( the fixed-width confidence interval), as well as MRPE (the minimum risk point estimation), of the work of \textit{M. Ghosh} and \textit{N. Mukhopadhyay} [Sankhyā, Ser. B 38, 203--218 (1976; Zbl 0409.62075)], in the context of estimating an unknown mean $$\mu$$ in a normal population $$N(\mu,\sigma^2)$$ having an unknown variance $$\sigma^2$$. An important extension is the use of sequential block sampling procedure, where the blocks are of fixed size $$k$$. In connection with the block approach, a more appropriate new standard deviation estimator is considered. Further, the article builds the whole array of estimation methodologies in order to address both FWCI and MRPE problems with appropriate first-order and second-order asymptotic analyses (see [\textit{J. K. Ghosh}, Higher order asymptotics. Hayward, CA: IMS, Institute of Mathematical Statistics (1994; Zbl 1163.62305)]). These are followed by extensive sets of carefully laid out data analyses assisted via large-scale computer simulations. These are wrapped up with illustrations using breast cancer data. Sequential change point test in the presence of outliers: the density power divergence based approach https://www.zbmath.org/1472.62131 2021-11-25T18:46:10.358925Z "Song, Junmo" https://www.zbmath.org/authors/?q=ai:song.junmo Summary: In this study, we consider a problem of monitoring parameter changes particularly in the presence of outliers. To propose a sequential procedure that is robust against outliers, we use the density power divergence to derive a detector and stopping time that make up our procedure. We first investigate the asymptotic properties of our sequential procedure for i.i.d. sequences and then extend the proposed procedure to stationary time series models, where we provide a set of sufficient conditions under which the proposed procedure has an asymptotically controlled size and consistency in power. As an application, our procedure is applied to the GARCH models. We demonstrate the validity and robustness of the proposed procedure through a simulation study. Finally, two real data analyses are provided to illustrate the usefulness of the proposed sequential procedure. Integer-valued time series model order shrinkage and selection via penalized quasi-likelihood approach https://www.zbmath.org/1472.62137 2021-11-25T18:46:10.358925Z "Wang, Xinyang" https://www.zbmath.org/authors/?q=ai:wang.xinyang "Wang, Dehui" https://www.zbmath.org/authors/?q=ai:wang.dehui "Yang, Kai" https://www.zbmath.org/authors/?q=ai:yang.kai Summary: This paper proposes a penalized maximum quasi-likelihood (PMQL) estimation that can solve the problem of order selection and parameter estimation regarding the $$p$$th-order integer-valued time series models. The PMQL estimation can effectively delete the insignificant orders in model. By contrast, the significant orders can be retained and their corresponding parameters are estimated, simultaneously. Moreover, the PMQL estimation possesses certain robustness hence its order shrinkage effectiveness is superior to the traditional penalized estimation method even if the data is contaminated. The theoretical properties of the PMQL estimator, including the consistency and oracle properties, are also investigated. Numerical simulation results show that our method is effective in a variety of situations. The Westgren's data set is also analyzed to illustrate the practicability of the PMQL method. Estimation error analysis of deep learning on the regression problem on the variable exponent Besov space https://www.zbmath.org/1472.62144 2021-11-25T18:46:10.358925Z "Tsuji, Kazuma" https://www.zbmath.org/authors/?q=ai:tsuji.kazuma "Suzuki, Taiji" https://www.zbmath.org/authors/?q=ai:suzuki.taiji Summary: Deep learning has achieved notable success in various fields, including image and speech recognition. One of the factors in the successful performance of deep learning is its high feature extraction ability. In this study, we focus on the adaptivity of deep learning; consequently, we treat the variable exponent Besov space, which has a different smoothness depending on the input location $$x$$. In other words, the difficulty of the estimation is not uniform within the domain. We analyze the general approximation error of the variable exponent Besov space and the approximation and estimation errors of deep learning. We note that the improvement based on adaptivity is remarkable when the region upon which the target function has less smoothness is small and the dimension is large. Moreover, the superiority to linear estimators is shown with respect to the convergence rate of the estimation error. Uniform convergence rate of the nonparametric maximum likelihood estimator for current status data with competing risks https://www.zbmath.org/1472.62145 2021-11-25T18:46:10.358925Z "Malov, Sergey V." https://www.zbmath.org/authors/?q=ai:malov.sergey-v Summary: We study the uniform convergence rate of the nonparametric maximum likelihood estimator (MLE) for the sub-distribution functions of failure times in the current status data with competing risks model. It is known that the MLE have $$L^2$$-norm convergence rate $$O_P (n^{-1/3})$$ in the absolutely continuous case, but no agreement has emerged on a uniform convergence rate. We specify conditions under which $$O_P (n^{-1/3 \log^{1/3} n})$$ is the uniform convergence rate for the MLE of the sub-distribution functions on finite intervals. The obtained result refines known uniform convergence rate in the particular case of current status data. The main result is applied in order to get the uniform convergence rate of the MLE for the survival function of failure time in the current status right-censored data model. Maximum multinomial likelihood estimation in compound mixture model with application to malaria study https://www.zbmath.org/1472.62155 2021-11-25T18:46:10.358925Z "Tian, Zhaoyang" https://www.zbmath.org/authors/?q=ai:tian.zhaoyang "Liang, Kun" https://www.zbmath.org/authors/?q=ai:liang.kun "Li, Pengfei" https://www.zbmath.org/authors/?q=ai:li.pengfei Summary: Malaria can be diagnosed by the presence of parasites and symptoms (usually fever) due to the parasites. In endemic areas, however, an individual may have fever attributable either to malaria or to other causes. Thus the parasite level of an individual with fever follows a two-component mixture, with the two components corresponding to malaria and nonmalaria individuals. Furthermore, the parasite levels of nonmalaria individuals can be characterised as a mixture of a zero component and a positive distribution. In this article, we propose a nonparametric maximum multinomial likelihood approach for estimating the proportion of malaria using parasite-level data from two groups of individuals collected in two different seasons. We develop an EM-algorithm to numerically calculate the proposed estimates and further establish their convergence rates. Simulation results show that the proposed estimators are more efficient than existing nonparametric estimators. The proposed method is used to analyse malaria survey data. Fast outlier removing method for point cloud of microscopic 3D measurement based on social circle https://www.zbmath.org/1472.62164 2021-11-25T18:46:10.358925Z "Cui, Haihua" https://www.zbmath.org/authors/?q=ai:cui.haihua "Wang, Qianjin" https://www.zbmath.org/authors/?q=ai:wang.qianjin "Dong, Dengfeng" https://www.zbmath.org/authors/?q=ai:dong.dengfeng "Wei, Hao" https://www.zbmath.org/authors/?q=ai:wei.hao "Zhang, Yihua" https://www.zbmath.org/authors/?q=ai:zhang.yihua Summary: Measurement outliers are easily caused by illumination, surface texture, human factors and so on during the process of microscopic topography measurement. These numerous cloud point noise will heavily affect instrument measurement accuracy and surface reconstruction quality. We propose a quick and accurate method for removing outliers based on social circle algorithm. First, the gaussian kernel function is used to calculate the voting value to determine the social circle's initial point, and then select the appropriate social circle radius and search window based on the initial point, and finally expand the social circle through an iterative method. Points which are not in the social circle can be considered as outliers and filtered out. The experimental results show the good performance of the algorithm with comparison to the existing filtering methods. The developed method has great potential in microscopic topography reconstruction, fitting and other point cloud processing tasks. Optimal prediction for high-dimensional functional quantile regression in reproducing kernel Hilbert spaces https://www.zbmath.org/1472.62177 2021-11-25T18:46:10.358925Z "Yang, Guangren" https://www.zbmath.org/authors/?q=ai:yang.guangren "Liu, Xiaohui" https://www.zbmath.org/authors/?q=ai:liu.xiaohui "Lian, Heng" https://www.zbmath.org/authors/?q=ai:lian.heng Summary: Regression problems with multiple functional predictors have been studied previously. In this paper, we investigate functional quantile linear regression with multiple functional predictors within the framework of reproducing kernel Hilbert spaces. The estimation procedure is based on an $$\ell_1$$-mixed-norm penalty. The learning rate of the estimator in prediction loss is established and a lower bound on the learning rate is also presented that matches the upper bound up to a logarithmic term. Spectral convergence of graph Laplacian and heat kernel reconstruction in $$L^\infty$$ from random samples https://www.zbmath.org/1472.62178 2021-11-25T18:46:10.358925Z "Dunson, David B." https://www.zbmath.org/authors/?q=ai:dunson.david-b "Wu, Hau-Tieng" https://www.zbmath.org/authors/?q=ai:wu.hau-tieng "Wu, Nan" https://www.zbmath.org/authors/?q=ai:wu.nan Summary: In the manifold setting, we provide a series of spectral convergence results quantifying how the eigenvectors and eigenvalues of the graph Laplacian converge to the eigenfunctions and eigenvalues of the Laplace-Beltrami operator in the $$L^\infty$$ sense. Based on these results, convergence of the proposed heat kernel approximation algorithm, as well as the convergence rate, to the exact heat kernel is guaranteed. To our knowledge, this is the first work exploring the spectral convergence in the $$L^\infty$$ sense and providing a numerical heat kernel reconstruction from the point cloud with theoretical guarantees. Online direct density-ratio estimation applied to inlier-based outlier detection https://www.zbmath.org/1472.68134 2021-11-25T18:46:10.358925Z "du Plessis, Marthinus Christoffel" https://www.zbmath.org/authors/?q=ai:du-plessis.marthinus-christoffel "Shiino, Hiroaki" https://www.zbmath.org/authors/?q=ai:shiino.hiroaki "Sugiyama, Masashi" https://www.zbmath.org/authors/?q=ai:sugiyama.masashi Summary: Many machine learning problems, such as nonstationarity adaptation, outlier detection, dimensionality reduction, and conditional density estimation, can be effectively solved by using the ratio of probability densities. Since the naive two-step procedure of first estimating the probability densities and then taking their ratio performs poorly, methods to directly estimate the density ratio from two sets of samples without density estimation have been extensively studied recently. However, these methods are batch algorithms that use the whole data set to estimate the density ratio, and they are inefficient in the online setup, where training samples are provided sequentially and solutions are updated incrementally without storing previous samples. In this letter, we propose two online density-ratio estimators based on the adaptive regularization of weight vectors. Through experiments on inlier-based outlier detection, we demonstrate the usefulness of the proposed methods. A comparative study of pairwise learning methods based on kernel ridge regression https://www.zbmath.org/1472.68158 2021-11-25T18:46:10.358925Z "Stock, Michiel" https://www.zbmath.org/authors/?q=ai:stock.michiel "Pahikkala, Tapio" https://www.zbmath.org/authors/?q=ai:pahikkala.tapio "Airola, Antti" https://www.zbmath.org/authors/?q=ai:airola.antti "De Baets, Bernard" https://www.zbmath.org/authors/?q=ai:de-baets.bernard "Waegeman, Willem" https://www.zbmath.org/authors/?q=ai:waegeman.willem Summary: Many machine learning problems can be formulated as predicting labels for a pair of objects. Problems of that kind are often referred to as pairwise learning, dyadic prediction, or network inference problems. During the past decade, kernel methods have played a dominant role in pairwise learning. They still obtain a state-of-the-art predictive performance, but a theoretical analysis of their behavior has been underexplored in the machine learning literature. In this work we review and unify kernel-based algorithms that are commonly used in different pairwise learning settings, ranging from matrix filtering to zero-shot learning. To this end, we focus on closed-form efficient instantiations of Kronecker kernel ridge regression. We show that independent task kernel ridge regression, two-step kernel ridge regression, and a linear matrix filter arise naturally as a special case of Kronecker kernel ridge regression, implying that all these methods implicitly minimize a squared loss. In addition, we analyze universality, consistency, and spectral filtering properties. Our theoretical results provide valuable insights into assessing the advantages and limitations of existing pairwise learning methods. Robust Farkas-Minkowski constraint qualification for convex inequality system under data uncertainty https://www.zbmath.org/1472.90078 2021-11-25T18:46:10.358925Z "Li, Xiao-Bing" https://www.zbmath.org/authors/?q=ai:li.xiaobing "Al-Homidan, Suliman" https://www.zbmath.org/authors/?q=ai:al-homidan.suliman-s "Ansari, Qamrul Hasan" https://www.zbmath.org/authors/?q=ai:ansari.qamrul-hasan "Yao, Jen-Chih" https://www.zbmath.org/authors/?q=ai:yao.jen-chih The authors consider the nonempty assumed solution set $$S=\{x\in \mathbb{R}^n \mid g_i(x,u_i)\le 0\; \forall\,u_i\in \mathcal{U}_i,\, i\in \mathcal{I}=1,2,\dots k \}$$ of a robust finite inequality system with compact convex uncertainty sets $$\mathcal{U}_i$$ and convex-concave finite valued functions $$g_i:\mathbb{R}^n\times\mathbb{R}^m\rightarrow\mathbb{R}$$, $$i\in \mathcal{I}$$. They show (Th. 1) that the robust global error bound (RGEB) $$\alpha \inf_{y\in S}\|x-y\|\le \sum_{i\in \mathcal{I}}[\sup_{u_i\in \mathcal{U}_i}g_i(x,u_i)]_+$$ on $$\mathbb{R}^n$$ for some $$\alpha>0$$ is sufficient for the validity of the robust Farkas-Minkowski constraint qualification (FMCQ) according to $$\mathrm{epi}\,\delta^*_S=\bigcup_{\lambda_i>0,\,\,u_i\in \mathcal{U}_i,\,i\in \mathcal{I}}\mathrm{epi}\,(\sum_{i\in \mathcal{I}}\lambda_ig_i(x,u_i))^*$$. $$\mathrm{epi} f$$ is the epigraph of an extended real-valued function $$f$$ and $$\delta^*_S$$ denotes the support functional of the convex set $$S$$. Hence the union is a closed convex cone. Example 3.2 demonstrates that the concavity of $$g_i$$ w.r.t. $$u_i$$ is essential. Conditions (FMCQ) and (REGB) are equivalent for the special case of in $$x$$ positively semidefinite quadratic forms $$g_i$$ with coefficients $$u_i$$ belonging to a scenario uncertainty set. In the last three rows of the proof of Th. 1, the subset sign should be replaced by the corresponding superset sign for getting equality. Maximum entropy on the mean approach to solve generalized inverse problems with an application in computational thermodynamics https://www.zbmath.org/1472.90088 2021-11-25T18:46:10.358925Z "Gamboa, Fabrice" https://www.zbmath.org/authors/?q=ai:gamboa.fabrice "Guéneau, Christine" https://www.zbmath.org/authors/?q=ai:gueneau.christine "Klein, Thierry" https://www.zbmath.org/authors/?q=ai:klein.thierry-e "Lawrence, Eva" https://www.zbmath.org/authors/?q=ai:lawrence.eva Summary: In this paper, we study entropy maximisation problems in order to reconstruct functions or measures subject to very general integral constraints. Our work has a twofold purpose. We first make a global synthesis of entropy maximisation problems in the case of a single reconstruction (measure or function) from the convex analysis point of view, as well as in the framework of the embedding into the Maximum Entropy on the Mean (MEM) setting. We further propose an extension of the entropy methods for a multidimensional case.