## Bai, Zhi-Dong

Compute Distance To:
 Author ID: bai.zhi-dong Published as: Bai, Zhidong; Bai, Z. D.; Bai, Zhi-Dong; Bai, Zhi Dong; Bai, ZhiDong; Bai, Zhi-dong Homepage: https://twas.org/sites/default/files/thth7_1.pdf External Links: MGP · Math-Net.Ru · dblp
 Documents Indexed: 234 Publications since 1981, including 6 Books 1 Contribution as Editor Reviewing Activity: 18 Reviews Biographic References: 2 Publications Co-Authors: 123 Co-Authors with 209 Joint Publications 4,828 Co-Co-Authors
all top 5

### Co-Authors

 19 single-authored 24 Zhao, Lincheng 18 Krishnaiah, Paruchuri Rama 16 Hu, Jiang 14 Rao, Calyampudi Radhakrishna 14 Yao, Jianfeng 14 Yin, Y.-Q. 13 Zheng, Shurong 12 Silverstein, Jack W. 9 Hu, Feifang 9 Miao, Bai-qi 8 Chen, Xiru 8 Wong, Wing-Keung 7 Pan, Guangming 6 Jiang, Dandan 6 Wang, Chen 6 Zhou, Wang 5 Chen, Guijing 5 Hwang, Hsien-Kuei 5 Li, Huiqin 5 Liang, Wenqi 5 Su, Chun 5 Wu, Yuehua 5 Yin, Yanqing 5 Zhang, Baoxue 4 Babu, Gutti Jogesh 4 Chen, Zehua 4 Jin, Baisuo 4 Li, Weiming 4 Liu, Tianqing 3 Cheng, Philip E. 3 Choi, Kwok Pui 3 Chow, Mosuk 3 He, Xuming 3 Hu, Guorong 3 Kundu, Debasis 3 Li, Hua 3 Liang, Yingchang 3 Liu, Huixia 3 Tsai, Tsung-Hsi 3 Tsay, Jhishen 3 Xia, Ningning 3 Zhang, Li-Xin 2 Chao, Chern-Ching 2 Chen, Jiaqi 2 Fu, James C. 2 Fujikoshi, Yasunori 2 Guo, Meihui 2 Harding, Matthew C. 2 Hui, Yongchang 2 Li, Gang 2 Nair, K. Krishnan 2 Qin, Yingli 2 Sarkar, Sanat Kumar 2 Subramanyam, Kasala 2 Wang, Wenjin 2 Wang, Xiaoying 2 Xu, Daming 2 Zen, Mei-Mei 2 Zhang, Bingzhi 2 Zhang, Chao 2 Zhang, Qiuyan 2 Zhao, Ningning 1 An, Hongzhi 1 Bai, Li 1 Biswas, Atanu 1 Brockwell, Peter J. 1 Chang, Lo-Bin 1 Chen, Changhua 1 Chen, Ling 1 Chen, Yang 1 Chen, Yuming 1 Chen, Yuming 1 Cheng, Yu 1 Couillet, Romain 1 Cui, Wenquan 1 Davis, Richard A. 1 Debbah, Mérouane 1 Devroye, Luc P. J. A. 1 Ding, Xue 1 Eddy, William F. 1 Fang, Zhaoben 1 Fu, Liya 1 Hou, Zhiqiang 1 Hsing, Tailen 1 Huang, Suyun 1 Hwang, Chii-Ruey 1 Lee, Sungchul 1 Li, Heng 1 Lin, Zhengyan 1 Lo Huang, Mong-Na 1 Lou, W. Y. Wendy 1 Luo, Wenya 1 Mangalam, Vasudevan 1 McAleer, Michael 1 Mitra, Amit 1 Mukherjee, Kanchan 1 Nandi, Swagata 1 Nishii, Ryuei 1 Niu, Zhenzhen 1 Penrose, Mathew D. ...and 24 more Co-Authors
all top 5

### Serials

 23 Journal of Multivariate Analysis 13 Statistics & Probability Letters 11 The Annals of Probability 11 Journal of Statistical Planning and Inference 11 Statistica Sinica 9 The Annals of Statistics 8 Bernoulli 7 The Annals of Applied Probability 6 Annals of the Institute of Statistical Mathematics 6 Sankhyā. Series A. Methods and Techniques 6 Scientia Sinica. Series A 6 Statistical Papers 4 Probability Theory and Related Fields 4 Electronic Journal of Probability 4 Science China. Mathematics 4 Random Matrices: Theory and Applications 3 IEEE Transactions on Information Theory 3 Acta Mathematica Sinica 3 Biometrika 3 Sankhyā. Series B. Methodological 3 Journal of Mathematical Research & Exposition 3 Chinese Annals of Mathematics. Series A 3 Communications in Statistics. Theory and Methods 3 Journal of the Korean Statistical Society 2 Journal of Statistical Physics 2 Teoriya Veroyatnosteĭ i eë Primeneniya 2 Theory of Probability and its Applications 2 Acta Mathematicae Applicatae Sinica 2 Chinese Annals of Mathematics. Series B 2 Statistics 2 Journal of Theoretical Probability 2 SIAM Journal on Matrix Analysis and Applications 2 Random Structures & Algorithms 2 Proceedings of the National Academy of Sciences of the United States of America 2 Stochastic Processes and their Applications 2 Kexue Tongbao 2 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 2 Test 1 Advances in Applied Probability 1 The Canadian Journal of Statistics 1 Physics Letters. A 1 Hiroshima Mathematical Journal 1 Journal of the American Statistical Association 1 Journal of Combinatorics, Information & System Sciences 1 Journal of Computational and Applied Mathematics 1 Mathematics and Computers in Simulation 1 Journal of Mathematics. Wuhan University 1 Journal of Time Series Analysis 1 Journal of Northeast Normal University. Natural Science Edition 1 Acta Mathematicae Applicatae Sinica. English Series 1 Science Exploration 1 Chinese Journal of Applied Probability and Statistics 1 Journal of China University of Science and Technology 1 Mathematical and Computer Modelling 1 Science in China. Series A 1 Computational Statistics and Data Analysis 1 Mathematical Methods of Statistics 1 Mathematical Finance 1 Australian & New Zealand Journal of Statistics 1 Far East Journal of Theoretical Statistics 1 The Econometrics Journal 1 Acta Mathematica Sinica. English Series 1 Quantitative Finance 1 International Mathematical Journal 1 Journal of Systems Science and Complexity 1 Acta Mathematica Scientia. Series A. (Chinese Edition) 1 Acta Mathematica Scientia. Series B. (English Edition) 1 Lecture Notes in Statistics 1 Cambridge Series in Statistical and Probabilistic Mathematics 1 Lecture Notes Series. Institute for Mathematical Sciences. National University of Singapore 1 Frontiers of Mathematics in China 1 Electronic Journal of Statistics 1 Sankhyā 1 Mathematics Monograph Series 1 Springer Series in Statistics
all top 5

### Fields

 184 Statistics (62-XX) 111 Probability theory and stochastic processes (60-XX) 41 Linear and multilinear algebra; matrix theory (15-XX) 14 Numerical analysis (65-XX) 11 Information and communication theory, circuits (94-XX) 3 Computer science (68-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 History and biography (01-XX) 2 Operator theory (47-XX) 2 Convex and discrete geometry (52-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 General and overarching topics; collections (00-XX) 1 Combinatorics (05-XX) 1 Astronomy and astrophysics (85-XX) 1 Biology and other natural sciences (92-XX)

### Citations contained in zbMATH Open

179 Publications have been cited 3,477 times in 1,951 Documents Cited by Year
Spectral analysis of large dimensional random matrices. 2nd ed. Zbl 1301.60002
Bai, Zhidong; Silverstein, Jack W.
2010
Effect of high dimension: by an example of a two sample problem. Zbl 0848.62030
Bai, Zhidong; Saranadasa, Hewa
1996
Methodologies in spectral analysis of large dimensional random matrices, a review. (With comments and rejoinder). Zbl 0949.60077
Bai, Z. D.
1999
CLT for linear spectral statistics of large-dimensional sample covariance matrices. Zbl 1063.60022
Bai, Z. D.; Silverstein, Jack W.
2004
Limit of the smallest eigenvalue of a large dimensional sample covariance matrix. Zbl 0779.60026
Bai, Z. D.; Yin, Y. Q.
1993
No eigenvalues outside the support of the limiting spectral distribution of large-dimensional sample covariance matrices. Zbl 0937.60017
Bai, Z. D.; Silverstein, Jack W.
1998
On the empirical distribution of eigenvalues of a class of large dimensional random matrices. Zbl 0833.60038
Silverstein, Jack W.; Bai, Z. D.
1995
On the limit of the largest eigenvalue of the large dimensional sample covariance matrix. Zbl 0627.62022
Yin, Y. Q.; Bai, Z. D.; Krishnaiah, P. R.
1988
Corrections to LRT on large-dimensional covariance matrix by RMT. Zbl 1360.62286
Bai, Zhidong; Jiang, Dandan; Yao, Jian-Feng; Zheng, Shurong
2009
Circular law. Zbl 0871.62018
Bai, Z. D.
1997
Spectral analysis of large dimensional random matrices. Zbl 1196.60002
Bai, Zhidong; Silverstein, Jack W.
2006
Ranked set sampling. Theory and applications. Zbl 1045.62007
Chen, Zehua; Bai, Zhidong; Sinha, Bimal K.
2004
Necessary and sufficient conditions for almost sure convergence of the largest eigenvalue of a Wigner matrix. Zbl 0677.60038
Bai, Z. D.; Yin, Y. Q.
1988
Central limit theorems for eigenvalues in a spiked population model. Zbl 1274.62129
Bai, Zhidong; Yao, Jian-Feng
2008
Marcinkiewicz strong laws for linear statistics. Zbl 0960.60026
Bai, Z. D.; Cheng, Philip E.
2000
$$M$$-estimation of multivariate linear regression parameters under a convex discrepancy function. Zbl 0820.62048
Bai, Z. D.; Rao, C. Radhakrishna; Wu, Y.
1992
A note on the largest eigenvalue of a large dimensional sample covariance matrix. Zbl 0652.60040
Bai, Z. D.; Silverstein, Jack W.; Yin, Y. Q.
1988
Large sample covariance matrices without independence structures in columns. Zbl 1135.62009
Bai, Zhidong; Zhou, Wang
2008
Asymptotic distributions of the maximal depth estimators for regression and multivariate location. Zbl 1007.62009
Bai, Zhi-Dong; He, Xuming
1999
Large sample covariance matrices and high-dimensional data analysis. Zbl 1380.62011
Yao, Jianfeng; Zheng, Shurong; Bai, Zhidong
2015
Asymptotics in randomized urn models. Zbl 1059.62111
Bai, Zhi-Dong; Hu, Feifang
2005
Convergence rate of expected spectral distributions of large random matrices. I: Wigner matrices. Zbl 0779.60024
Bai, Z. D.
1993
On detection of the number of signals in presence of white noise. Zbl 0617.62055
Zhao, L. C.; Krishnaiah, P. R.; Bai, Z. D.
1986
Asymptotic theorems for urn models with nonhomogeneous generating matrices. Zbl 0954.62014
Bai, Z. D.; Hu, Feifang
1999
Kernel estimators of density function of directional data. Zbl 0669.62015
Bai, Z. D.; Rao, C. Radhakrishna; Zhao, L. C.
1988
Convergence to the semicircle law. Zbl 0648.60030
Bai, Z. D.; Yin, Y. Q.
1988
Convergence rate of expected spectral distributions of large random matrices. II: Sample covariance matrices. Zbl 0779.60025
Bai, Z. D.
1993
On sample eigenvalues in a generalized spiked population model. Zbl 1301.62049
Bai, Zhidong; Yao, Jianfeng
2012
On asymptotics of eigenvectors of large sample covariance matrix. Zbl 1162.15012
Bai, Z. D.; Miao, B. Q.; Pan, G. M.
2007
On the convergence of the spectral empirical process of Wigner matrices. Zbl 1101.60012
Bai, Z. D.; Yao, J.
2005
Exact separation of eigenvalues of large dimensional sample covariance matrices. Zbl 0964.60041
Bai, Z. D.; Silverstein, Jack W.
1999
Enhancement of the applicability of Markowitz’s portfolio optimization by utilizing random matrix theory. Zbl 1185.91155
Bai, Zhidong; Liu, Huixia; Wong, Wing-Keung
2009
Substitution principle for CLT of linear spectral statistics of high-dimensional sample covariance matrices with applications to hypothesis testing. Zbl 1312.62074
Zheng, Shurong; Bai, Zhidong; Yao, Jianfeng
2015
Probability inequalities. Zbl 1221.60001
Lin, Zhengyan; Bai, Zhidong
2010
The complete convergence for partial sums of i.i.d. random variables. Zbl 0554.60039
Bai, Zhidong; Su, Chun
1985
Asymptotic properties of adaptive designs for clinical trials with delayed response. Zbl 1012.62087
Bai, Z. D.; Hu, Feifang; Rosenberger, William F.
2002
Gaussian approximation theorems for urn models and their applications. Zbl 1014.60025
Bai, Z. D.; Hu, Feifang; Zhang, Li-Xin
2002
Asymptotic theory of least distances estimate in multivariate linear models. Zbl 0714.62048
Bai, Z. D.; Chen, X. R.; Miao, B. Q.; Rao, C. Radhakrishna
1990
On detection of the number of signals when the noise covariance matrix is arbitrary. Zbl 0617.62056
Zhao, L. C.; Krishnaiah, P. R.; Bai, Z. D.
1986
Convergence rates of spectral distributions of large sample covariance matrices. Zbl 1059.60036
Bai, Z. D.; Miao, Baiqi; Yao, Jian-feng
2003
On estimation of the population spectral distribution from a high-dimensional sample covariance matrix. Zbl 1373.62245
Bai, Zhidong; Chen, Jiaqi; Yao, Jianfeng
2010
On rates of convergence of efficient detection criteria in signal processing with white noise. Zbl 0677.94001
Bai, Zhi-Dong; Krishnaiah, Paruchuri R.; Zhao, Lin-Cheng
1989
Testing the independence of sets of large-dimensional variables. Zbl 1256.62033
Jiang, DanDan; Bai, ZhiDong; Zheng, ShuRong
2013
Limiting behavior of the norm of products of random matrices and two problems of Geman-Hwang. Zbl 0586.60021
Bai, Z. D.; Yin, Y. Q.
1986
Limiting behavior of $$M$$-estimators of regression coefficients in high dimensional linear models. I: Scale-dependent case. II: Scale-invariant case. Zbl 0816.62025
Bai, Z. D.; Wu, Y.
1994
On testing the equality of high dimensional mean vectors with unequal covariance matrices. Zbl 1396.62106
Hu, Jiang; Bai, Zhidong; Wang, Chen; Wang, Wei
2017
Convergence rates of the spectral distributions of large Wigner matrices. Zbl 0987.60050
Bai, Z. D.; Miao, Baiqi; Tsay, Jhishen
2002
CLT for linear spectral statistics of Wigner matrices. Zbl 1188.15032
Bai, Zhidong; Wang, Xiaoying; Zhou, Wang
2009
A review of 20 years of naive tests of significance for high-dimensional mean vectors and covariance matrices. Zbl 1360.62290
Hu, Jiang; Bai, ZhiDong
2016
Limiting spectral distribution of a symmetrized auto-cross covariance matrix. Zbl 1296.60006
Jin, Baisuo; Wang, Chen; Bai, Z. D.; Nair, K. Krishnan; Harding, Matthew
2014
Limiting behavior of the eigenvalues of a multivariate F matrix. Zbl 0531.62018
Yin, Y. Q.; Bai, Z. D.; Krishnaiah, P. R.
1983
Testing linear hypotheses in high-dimensional regressions. Zbl 1440.62215
Bai, Zhidong; Jiang, Dandan; Yao, Jian-Feng; Zheng, Shurong
2013
An efficient algorithm for estimating the parameters of superimposed exponential signals. Zbl 1030.62062
Bai, Z. D.; Rao, C. R.; Chow, M.; Kundu, D.
2003
Maxima in hypercubes. Zbl 1080.60007
Bai, Zhi-Dong; Devroye, Luc; Hwang, Hsien-Kuei; Tsai, Tsung-Hsi
2005
An adaptive design for multi-arm clinical trials. Zbl 1011.62079
Bai, Z. D.; Hu, Feifang; Shen, Liang
2002
No eigenvalues outside the support of the limiting spectral distribution of information-plus-noise type matrices. Zbl 1248.15028
Bai, Zhidong; Silverstein, Jack W.
2012
Model selection with data-oriented penalty. Zbl 0926.62045
Bai, Z. D.; Rao, C. R.; Wu, Y.
1999
Functional CLT for sample covariance matrices. Zbl 1210.60025
Bai, Zhidong; Wang, Xiaoying; Zhou, Wang
2010
Estimation of spiked eigenvalues in spiked models. Zbl 1251.15037
Bai, Zhidong; Ding, Xue
2012
On the semicircular law of large-dimensional random quaternion matrices. Zbl 1353.60024
Yin, Yanqing; Bai, Zhidong; Hu, Jiang
2016
General $$M$$-estimation. Zbl 0890.62050
Bai, Z. D.; Wu, Y.
1997
On the limiting empirical distribution function of the eigenvalues of a multivariate F matrix. Zbl 0676.62021
Bai, Z. D.; Yin, Y. Q.; Krishnaiah, P. R.
1987
Consistency of AIC and BIC in estimating the number of significant components in high-dimensional principal component analysis. Zbl 1395.62119
Bai, Zhidong; Choi, Kwok Pui; Fujikoshi, Yasunori
2018
On limiting spectral distribution of product of two random matrices when the underlying distribution is isotropic. Zbl 0657.62058
Bai, Z. D.; Yin, Y. Q.; Krishnaiah, P. R.
1986
A theorem of Feller revisited. Zbl 0669.60034
Bai, Z. D.
1989
On limit theorem for the eigenvalues of product of two random matrices. Zbl 1108.15022
Bai, Z. D.; Miao, Baiqi; Jin, Baisuo
2007
Edgeworth expansion of a function of sample means. Zbl 0741.62016
Bai, Z. D.; Rao, C. Radhakrishna
1991
On the theory of ranked-set sampling and its ramifications. Zbl 1008.62023
Bai, Zhidong; Chen, Zehua
2003
Normal approximations of the number of records in geometrically distributed random variables. Zbl 0961.60040
Bai, Zhi-Dong; Hwang, Hsien-Kuei; Liang, Wen-Qi
1998
Strong consistency of the information criterion for model selection in multivariate analysis. Zbl 0678.62064
Nishii, Ryuei; Bai, Zhidong; Krishnaiah, Paruchuri R.
1988
Analysis of rounded data from dependent sequences. Zbl 1432.62065
Zhang, Baoxue; Liu, Tianqing; Bai, Z. D.
2010
Statistical analysis for rounded data. Zbl 1162.62012
Bai, Zhidong; Zheng, Shurong; Zhang, Baoxue; Hu, Guorong
2009
Asymptotic normality of minimum $$L_ 1$$-norm estimates in linear models. Zbl 0728.62068
Chen, Xiru; Bai, Zhidong; Zao, Lincheng; Wu, Yuehua
1990
On the variance of the number of maxima in random vectors and its applications. Zbl 0941.60021
Bai, Zhi-Dong; Chao, Chern-Ching; Hwang, Hsien-Kuei; Liang, Wen-Qi
1998
A note on the convergence rate of the spectral distributions of large random matrices. Zbl 0894.60034
Bai, Z. D.; Miao, Baiqi; Tsay, Jhishen
1997
Limit theorems for the number of maxima in random samples from planar regions. Zbl 0986.60007
Bai, Zhi-Dong; Hwang, Hsien-Kuei; Liang, Wen-Qi; Tsai, Tsung-Hsi
2001
Mixtures of global and local Edgeworth expansions and their applications. Zbl 0864.62006
Babu, Gutti Jogesh; Bai, Z. D.
1996
A chi-square test for dimensionality with non-Gaussian data. Zbl 1032.62054
Bai, Z. D.; He, Xuming
2004
On the limit of extreme eigenvalues of large dimensional random quaternion matrices. Zbl 1331.15022
Yin, Yanqing; Bai, Zhidong; Hu, Jiang
2014
Limiting behavior of eigenvectors of large Wigner matrices. Zbl 1235.82035
Bai, Z. D.; Pan, G. M.
2012
The optimal ranked-set sampling scheme for parametric families. Zbl 0972.62053
Chen, Zehua; Bai, Zhidong
2000
The exact and limiting distributions for the number of successes in success runs within a sequence of Markov-dependent two-state trials. Zbl 1067.60064
Fu, James C.; Lou, W. Y. Wendy; Bai, Zhi-Dong; Li, Gang
2002
An extension of the Hardy-Littlewood strong law. Zbl 1067.60501
Bai, Zhidong; Cheng, Philip E.; Zhang, Cun-Hui
1997
Eigen-inference for energy estimation of multiple sources. Zbl 1366.62107
Couillet, Romain; Silverstein, Jack W.; Bai, Zhidong; Debbah, Mérouane
2011
Inference on multiple correlation coefficients with moderately high dimensional data. Zbl 1336.62157
Zheng, Shurong; Jiang, Dandan; Bai, Zhidong; He, Xuming
2014
Convergence rates of the spectral distributions of large random quaternion self-dual Hermitian matrices. Zbl 1309.15055
Yin, Yanqing; Bai, Zhidong
2014
Least absolute deviations analysis of variance. Zbl 0727.62073
Bai, Z. D.; Radhakrishna Rao, C.; Yin, Y. Q.
1990
Rooted edges of a minimal directed spanning tree on random points. Zbl 1094.60004
Bai, Z. D.; Lee, Sungchul; Penrose, Mathew D.
2006
Asymptotic properties of eigenmatrices of a large sample covariance matrix. Zbl 1234.15013
Bai, Z. D.; Liu, H. X.; Wong, W. K.
2011
CLT for eigenvalue statistics of large-dimensional general Fisher matrices with applications. Zbl 1375.60066
Zheng, Shurong; Bai, Zhidong; Yao, Jianfeng
2017
Estimation of the population spectral distribution from a large dimensional sample covariance matrix. Zbl 1278.62079
Li, Weiming; Chen, Jiaqi; Qin, Yingli; Bai, Zhidong; Yao, Jianfeng
2013
Rank regression for analysis of clustered data: a natural induced smoothing approach. Zbl 1464.62074
Fu, Liya; Wang, You-Gan; Bai, Zhidong
2010
Analysis of rounded data in mixture normal model. Zbl 1254.62023
Zhao, Ningning; Bai, Zhidong
2012
Semicircle law for Hadamard products. Zbl 1139.15012
Bai, Z. D.; Zhang, L. X.
2008
Convergence rates of eigenvector empirical spectral distribution of large dimensional sample covariance matrix. Zbl 1285.15018
Xia, Ningning; Qin, Yingli; Bai, Zhidong
2013
On limiting empirical distribution function of the eigenvalues of a multivariate F matrix. Zbl 0635.62018
Bai, Z. D.; Yin, Y. Q.; Krishnaiah, P. R.
1987
Convergence of the empirical spectral distribution function of beta matrices. Zbl 1319.60006
Bai, Zhidong; Hu, Jiang; Pan, Guangming; Zhou, Wang
2015
On the maximum-likelihood estimator for the location parameter of a Cauchy distribution. Zbl 0624.62032
Bai, Z. D.; Fu, J. C.
1987
The limiting spectral distribution of the product of the Wigner matrix and a nonnegative definite matrix. Zbl 1200.15020
Bai, Z. D.; Zhang, L. X.
2010
Extreme eigenvalues of large dimensional quaternion sample covariance matrices. Zbl 1311.60036
Li, Huiqin; Bai, Zhidong
2015
Generalized four moment theorem and an application to CLT for spiked eigenvalues of high-dimensional covariance matrices. Zbl 1475.60014
Jiang, Dandan; Bai, Zhidong
2021
Central limit theorem for linear spectral statistics of large dimensional separable sample covariance matrices. Zbl 1466.60008
Bai, Zhidong; Li, Huiqin; Pan, Guangming
2019
Invariant test based on the modified correction to LRT for the equality of two high-dimensional covariance matrices. Zbl 1418.62242
Zhang, Qiuyan; Hu, Jiang; Bai, Zhidong
2019
Convergence rate of eigenvector empirical spectral distribution of large Wigner matrices. Zbl 1420.62235
Xia, Ningning; Bai, Zhidong
2019
On LR simultaneous test of high-dimensional mean vector and covariance matrix under non-normality. Zbl 1407.62203
Niu, Zhenzhen; Hu, Jiang; Bai, Zhidong; Gao, Wei
2019
Consistency of AIC and BIC in estimating the number of significant components in high-dimensional principal component analysis. Zbl 1395.62119
Bai, Zhidong; Choi, Kwok Pui; Fujikoshi, Yasunori
2018
Limiting behavior of eigenvalues in high-dimensional MANOVA via RMT. Zbl 1411.62130
Bai, Zhidong; Choi, Kwok Pui; Fujikoshi, Yasunori
2018
Estimating the number of sources in magnetoencephalography using spiked population eigenvalues. Zbl 1398.62353
Yao, Zhigang; Zhang, Ye; Bai, Zhidong; Eddy, William F.
2018
A central limit theorem for sums of functions of residuals in a high-dimensional regression model with an application to variance homoscedasticity test. Zbl 1420.62291
Bai, Zhidong; Pan, Guangming; Yin, Yanqing
2018
Multi-sample test for high-dimensional covariance matrices. Zbl 07416439
Zhang, Chao; Bai, Zhidong; Hu, Jiang; Wang, Chen
2018
On testing the equality of high dimensional mean vectors with unequal covariance matrices. Zbl 1396.62106
Hu, Jiang; Bai, Zhidong; Wang, Chen; Wang, Wei
2017
CLT for eigenvalue statistics of large-dimensional general Fisher matrices with applications. Zbl 1375.60066
Zheng, Shurong; Bai, Zhidong; Yao, Jianfeng
2017
Test on the linear combinations of mean vectors in high-dimensional data. Zbl 1369.62122
Li, Huiqin; Hu, Jiang; Bai, Zhidong; Yin, Yanqing; Zou, Kexin
2017
A review of 20 years of naive tests of significance for high-dimensional mean vectors and covariance matrices. Zbl 1360.62290
Hu, Jiang; Bai, ZhiDong
2016
On the semicircular law of large-dimensional random quaternion matrices. Zbl 1353.60024
Yin, Yanqing; Bai, Zhidong; Hu, Jiang
2016
Convergence of empirical spectral distributions of large dimensional quaternion sample covariance matrices. Zbl 1400.60007
Li, Huiqin; Bai, Zhi Dong; Hu, Jiang
2016
Large sample covariance matrices and high-dimensional data analysis. Zbl 1380.62011
Yao, Jianfeng; Zheng, Shurong; Bai, Zhidong
2015
Substitution principle for CLT of linear spectral statistics of high-dimensional sample covariance matrices with applications to hypothesis testing. Zbl 1312.62074
Zheng, Shurong; Bai, Zhidong; Yao, Jianfeng
2015
Convergence of the empirical spectral distribution function of beta matrices. Zbl 1319.60006
Bai, Zhidong; Hu, Jiang; Pan, Guangming; Zhou, Wang
2015
Extreme eigenvalues of large dimensional quaternion sample covariance matrices. Zbl 1311.60036
Li, Huiqin; Bai, Zhidong
2015
Functional CLT of eigenvectors for large sample covariance matrices. Zbl 1309.15054
Xia, Ningning; Bai, Zhidong
2015
A note on the limiting spectral distribution of a symmetrized auto-cross covariance matrix. Zbl 1333.60025
Bai, Zhidong; Wang, Chen
2015
Strong limit of the extreme eigenvalues of a symmetrized auto-cross covariance matrix. Zbl 1328.60088
Wang, Chen; Jin, Baisuo; Bai, Z. D.; Nair, K. Krishnan; Harding, Matthew
2015
Convergence rates of spectral distributions of large dimensional quaternion sample covariance matrices. Zbl 1312.15052
Li, Huiqin; Bai, Zhidong
2015
Stochastic dominance statistics for risk averters and risk seekers: an analysis of stock preferences for USA and China. Zbl 1398.62276
Bai, Zhidong; Li, Hua; McAleer, Michael; Wong, Wing-Keung
2015
Limiting spectral distribution of a symmetrized auto-cross covariance matrix. Zbl 1296.60006
Jin, Baisuo; Wang, Chen; Bai, Z. D.; Nair, K. Krishnan; Harding, Matthew
2014
On the limit of extreme eigenvalues of large dimensional random quaternion matrices. Zbl 1331.15022
Yin, Yanqing; Bai, Zhidong; Hu, Jiang
2014
Inference on multiple correlation coefficients with moderately high dimensional data. Zbl 1336.62157
Zheng, Shurong; Jiang, Dandan; Bai, Zhidong; He, Xuming
2014
Convergence rates of the spectral distributions of large random quaternion self-dual Hermitian matrices. Zbl 1309.15055
Yin, Yanqing; Bai, Zhidong
2014
CLT for linear spectral statistics of a rescaled sample precision matrix. Zbl 1330.15045
Zheng, Shurong; Bai, Zhidong; Yao, Jianfeng
2014
Spectral theory of large dimensional random matrices and its applications to wireless communications and finance statistics. Random matrix theory and its applications. Zbl 1288.15046
Bai, Zhidong; Fang, Zhaoben; Liang, Ying-Chang
2014
Testing the independence of sets of large-dimensional variables. Zbl 1256.62033
Jiang, DanDan; Bai, ZhiDong; Zheng, ShuRong
2013
Testing linear hypotheses in high-dimensional regressions. Zbl 1440.62215
Bai, Zhidong; Jiang, Dandan; Yao, Jian-Feng; Zheng, Shurong
2013
Estimation of the population spectral distribution from a large dimensional sample covariance matrix. Zbl 1278.62079
Li, Weiming; Chen, Jiaqi; Qin, Yingli; Bai, Zhidong; Yao, Jianfeng
2013
Convergence rates of eigenvector empirical spectral distribution of large dimensional sample covariance matrix. Zbl 1285.15018
Xia, Ningning; Qin, Yingli; Bai, Zhidong
2013
Asymptotic error bounds for kernel-based Nyström low-rank approximation matrices. Zbl 1349.62262
Chang, Lo-Bin; Bai, Zhidong; Huang, Su-Yun; Hwang, Chii-Ruey
2013
On sample eigenvalues in a generalized spiked population model. Zbl 1301.62049
Bai, Zhidong; Yao, Jianfeng
2012
No eigenvalues outside the support of the limiting spectral distribution of information-plus-noise type matrices. Zbl 1248.15028
Bai, Zhidong; Silverstein, Jack W.
2012
Estimation of spiked eigenvalues in spiked models. Zbl 1251.15037
Bai, Zhidong; Ding, Xue
2012
Limiting behavior of eigenvectors of large Wigner matrices. Zbl 1235.82035
Bai, Z. D.; Pan, G. M.
2012
Analysis of rounded data in mixture normal model. Zbl 1254.62023
Zhao, Ningning; Bai, Zhidong
2012
Rounded data analysis based on ranked set sample. Zbl 1440.62086
Li, Weiming; Liu, Tianqing; Bai, Zhidong
2012
Convergence rates to the Marchenko-Pastur type distribution. Zbl 1234.60033
Bai, Zhidong; Hu, Jiang; Zhou, Wang
2012
Eigen-inference for energy estimation of multiple sources. Zbl 1366.62107
Couillet, Romain; Silverstein, Jack W.; Bai, Zhidong; Debbah, Mérouane
2011
Asymptotic properties of eigenmatrices of a large sample covariance matrix. Zbl 1234.15013
Bai, Z. D.; Liu, H. X.; Wong, W. K.
2011
A note on rate of convergence in probability to semicircular law. Zbl 1244.60022
Bai, Zhidong; Hu, Jiang; Pan, Guangming; Zhou, Wang
2011
Rounded data analysis based on multi-layer ranked set sampling. Zbl 1271.62118
Li, Wei Ming; Bai, Zhi Dong
2011
The mean-variance ratio test – a complement to the coefficient of variation test and the Sharpe ratio test. Zbl 1219.62030
Bai, Zhidong; Wang, Keyan; Wong, Wing-Keung
2011
Super efficient frequency estimation. Zbl 1213.62098
Kundu, Debasis; Bai, Zhidong; Nandi, Swagata; Bai, Li
2011
Analysis of accumulated rounding errors in autoregressive processes. Zbl 1294.62182
Li, Weiming; Bai, Z. D.
2011
Multivariate causality tests with simulation and application. Zbl 1219.62094
Bai, Zhidong; Li, Heng; Wong, Wing-Keung; Zhang, Bingzhi
2011
Test statistics for prospect and Markowitz stochastic dominances with applications. Zbl 1219.91149
Bai, Zhidong; Li, Hua; Liu, Huixia; Wong, Wing-Keung
2011
Spectral analysis of large dimensional random matrices. 2nd ed. Zbl 1301.60002
Bai, Zhidong; Silverstein, Jack W.
2010
Probability inequalities. Zbl 1221.60001
Lin, Zhengyan; Bai, Zhidong
2010
On estimation of the population spectral distribution from a high-dimensional sample covariance matrix. Zbl 1373.62245
Bai, Zhidong; Chen, Jiaqi; Yao, Jianfeng
2010
Functional CLT for sample covariance matrices. Zbl 1210.60025
Bai, Zhidong; Wang, Xiaoying; Zhou, Wang
2010
Analysis of rounded data from dependent sequences. Zbl 1432.62065
Zhang, Baoxue; Liu, Tianqing; Bai, Z. D.
2010
Rank regression for analysis of clustered data: a natural induced smoothing approach. Zbl 1464.62074
Fu, Liya; Wang, You-Gan; Bai, Zhidong
2010
The limiting spectral distribution of the product of the Wigner matrix and a nonnegative definite matrix. Zbl 1200.15020
Bai, Z. D.; Zhang, L. X.
2010
Multivariate linear and nonlinear causality tests. Zbl 1201.62072
Bai, Zhidong; Wong, Wing-Keung; Zhang, Bingzhi
2010
Revisit of Sheppard corrections in linear regression. Zbl 1207.62123
Liu, TianQing; Zhang, BaoXue; Hu, GuoRong; Bai, ZhiDong
2010
Corrections to LRT on large-dimensional covariance matrix by RMT. Zbl 1360.62286
Bai, Zhidong; Jiang, Dandan; Yao, Jian-Feng; Zheng, Shurong
2009
Enhancement of the applicability of Markowitz’s portfolio optimization by utilizing random matrix theory. Zbl 1185.91155
Bai, Zhidong; Liu, Huixia; Wong, Wing-Keung
2009
CLT for linear spectral statistics of Wigner matrices. Zbl 1188.15032
Bai, Zhidong; Wang, Xiaoying; Zhou, Wang
2009
Statistical analysis for rounded data. Zbl 1162.62012
Bai, Zhidong; Zheng, Shurong; Zhang, Baoxue; Hu, Guorong
2009
Random matrix theory and its applications. Multivariate statistics and wireless communications. Zbl 1176.15001
2009
Central limit theorems for eigenvalues in a spiked population model. Zbl 1274.62129
Bai, Zhidong; Yao, Jian-Feng
2008
Large sample covariance matrices without independence structures in columns. Zbl 1135.62009
Bai, Zhidong; Zhou, Wang
2008
Semicircle law for Hadamard products. Zbl 1139.15012
Bai, Z. D.; Zhang, L. X.
2008
Statistical analysis for rounded data. Zbl 1269.62035
Bai, Zhidong; Zheng, Shurong; Zhang, Baoxue; Hu, Guorong
2008
On constrained M-estimation and its recursive analog in multivariate linear regression models. Zbl 1135.62045
Bai, Zhidong; Chen, Xiru; Wu, Yuehua
2008
On asymptotics of eigenvectors of large sample covariance matrix. Zbl 1162.15012
Bai, Z. D.; Miao, B. Q.; Pan, G. M.
2007
On limit theorem for the eigenvalues of product of two random matrices. Zbl 1108.15022
Bai, Z. D.; Miao, Baiqi; Jin, Baisuo
2007
On the signal-to-interference ratio of CDMA systems in wireless communications. Zbl 1133.94012
Bai, Z. D.; Silverstein, Jack W.
2007
Statistics with estimated parameters. Zbl 1128.62026
Yang, Z. L.; Tse, Y. K.; Bai, Z. D.
2007
A generalized confidence interval for the difference of the means of two normal populations. Zbl 1133.62018
Tao, Jian; Biswas, Atanu; Bai, Zhi-Dong
2007
Spectral analysis of large dimensional random matrices. Zbl 1196.60002
Bai, Zhidong; Silverstein, Jack W.
2006
Rooted edges of a minimal directed spanning tree on random points. Zbl 1094.60004
Bai, Z. D.; Lee, Sungchul; Penrose, Mathew D.
2006
Asymptotics in randomized urn models. Zbl 1059.62111
Bai, Zhi-Dong; Hu, Feifang
2005
On the convergence of the spectral empirical process of Wigner matrices. Zbl 1101.60012
Bai, Z. D.; Yao, J.
2005
Maxima in hypercubes. Zbl 1080.60007
Bai, Zhi-Dong; Devroye, Luc; Hwang, Hsien-Kuei; Tsai, Tsung-Hsi
2005
The broken sample problem. Zbl 1062.62041
Bai, Zhidong; Hsing, Tailen
2005
CLT for linear spectral statistics of large-dimensional sample covariance matrices. Zbl 1063.60022
Bai, Z. D.; Silverstein, Jack W.
2004
Ranked set sampling. Theory and applications. Zbl 1045.62007
Chen, Zehua; Bai, Zhidong; Sinha, Bimal K.
2004
A chi-square test for dimensionality with non-Gaussian data. Zbl 1032.62054
Bai, Z. D.; He, Xuming
2004
Convergence rates of spectral distributions of large sample covariance matrices. Zbl 1059.60036
Bai, Z. D.; Miao, Baiqi; Yao, Jian-feng
2003
An efficient algorithm for estimating the parameters of superimposed exponential signals. Zbl 1030.62062
Bai, Z. D.; Rao, C. R.; Chow, M.; Kundu, D.
2003
On the theory of ranked-set sampling and its ramifications. Zbl 1008.62023
Bai, Zhidong; Chen, Zehua
2003
Weighted $$W$$ test for normality and asymptotics a revisit of Chen–Shapiro test for normality. Zbl 1026.62042
Bai, Z. D.; Chen, Ling
2003
Berry-{E}sseen bounds for the number of maxima in planar regions. Zbl 1065.60020
Bai, Zhi-Dong; Hwang, Hsien-Kuei; Tsai, Tsung-Hsi
2003
Convergence rate of the best-$$r$$-point-average estimator for the maximizer of a nonparametric regression function. Zbl 1140.62320
Bai, Zhidong; Chen, Zehua; Wu, Yaohua
2003
Asymptotic properties of adaptive designs for clinical trials with delayed response. Zbl 1012.62087
Bai, Z. D.; Hu, Feifang; Rosenberger, William F.
2002
Gaussian approximation theorems for urn models and their applications. Zbl 1014.60025
Bai, Z. D.; Hu, Feifang; Zhang, Li-Xin
2002
Convergence rates of the spectral distributions of large Wigner matrices. Zbl 0987.60050
Bai, Z. D.; Miao, Baiqi; Tsay, Jhishen
2002
An adaptive design for multi-arm clinical trials. Zbl 1011.62079
Bai, Z. D.; Hu, Feifang; Shen, Liang
2002
The exact and limiting distributions for the number of successes in success runs within a sequence of Markov-dependent two-state trials. Zbl 1067.60064
Fu, James C.; Lou, W. Y. Wendy; Bai, Zhi-Dong; Li, Gang
2002
R-estimation in autoregression with square-integrable score function. Zbl 1011.62093
Mukherjee, Kanchan; Bai, Z. D.
2002
Limit theorems for the number of maxima in random samples from planar regions. Zbl 0986.60007
Bai, Zhi-Dong; Hwang, Hsien-Kuei; Liang, Wen-Qi; Tsai, Tsung-Hsi
2001
Limit theorems in an urn model with time trends in sequential experiment. Zbl 0998.62517
Bai, Zhidong; Chen, Guijing; Hu, Feifang
2001
A kind of urn model for adaptive sequential design. Zbl 1162.62398
Bai, Zhidong; Chen, Guijing; Hu, Feifang
2001
...and 79 more Documents
all top 5

### Cited by 2,135 Authors

 96 Bai, Zhi-Dong 33 Pan, Guangming 29 Yao, Jianfeng 28 Bose, Arup 26 Zhou, Wang 24 Götze, Friedrich 22 Jiang, Tiefeng 22 Zheng, Shurong 21 Hu, Feifang 20 Erdős, László 20 Hu, Jiang 20 Tikhomirov, Alexander Nikolaevich 20 Zhang, Li-Xin 19 Aoshima, Makoto 19 Silverstein, Jack W. 19 Yata, Kazuyoshi 18 Vu, Van H. 15 Fujikoshi, Yasunori 15 Sung, Soohak 14 Chen, Pingyan 14 Li, Weiming 14 Zhao, Lincheng 13 Bordenave, Charles 13 O’Rourke, Sean D. 13 Péché, Sandrine 13 Wu, Yuehua 13 Yin, Yanqing 12 Chafaï, Djalil 12 Cui, Hengjian 12 El Karoui, Noureddine 12 Kundu, Debasis 12 Miao, Bai-qi 12 Soshnikov, Alexander B. 11 Bao, Zhigang 11 Couillet, Romain 11 Jin, Baisuo 11 Krüger, Torben 11 Tao, Terence 11 Wang, Xuejun 11 Wong, Wing-Keung 10 Benaych-Georges, Florent 10 Bodnar, Taras 10 Guionnet, Alice 10 Jafari Jozani, Mohammad 10 Jiang, Dandan 10 Ledoit, Olivier 10 Modarres, Reza 10 Najim, Jamal 10 Tikhomirov, Konstantin E. 10 Yin, Jun 10 Zou, Changliang 9 Baik, Jinho 9 Capitaine, Mireille 9 Hachem, Walid 9 Litvak, Aleksandr Evgen’evich 9 Qi, Yongcheng 9 Rao, Calyampudi Radhakrishna 9 Renfrew, David 9 Rudelson, Mark 9 Vershynin, Roman 9 Wolf, Michael 9 Xie, Junshan 9 Zhang, Jinting 9 Zuo, Yijun 8 Adamczak, Radosław 8 Balakrishnan, Narayanaswamy 8 Basak, Anirban 8 Dette, Holger 8 Ding, Xue 8 Dobriban, Edgar 8 Feng, Long 8 Harrar, Solomon W. 8 Heiny, Johannes 8 Li, Runze 8 Lin, Zhengyan 8 Liu, Baisen 8 Naumov, Alekseĭ Aleksandrovich 8 Parolya, Nestor R. 8 Paul, Debashis 8 Rousseeuw, Peter J. 8 Saha, Koushik 8 Tomczak-Jaegermann, Nicole 8 Wang, Chen 8 Wu, Wei Biao 8 Wu, Yaohua 8 Yau, Horng-Tzer 7 Ding, Xiucai 7 Hazra, Rajat Subhra 7 He, Xuming 7 Ishii, Aki 7 Johnstone, Iain Murray 7 Krishnaiah, Paruchuri Rama 7 Lachos Dávila, Víctor Hugo 7 Li, Huiqin 7 Lytova, Anna 7 Nechita, Ion 7 Pastur, Leonid Andreevich 7 Shen, Aiting 7 Wang, Shaochen 7 Wang, Zhaojun ...and 2,035 more Authors
all top 5

### Cited in 274 Serials

 180 Journal of Multivariate Analysis 130 The Annals of Statistics 86 Journal of Statistical Planning and Inference 85 Statistics & Probability Letters 80 Random Matrices: Theory and Applications 62 Computational Statistics and Data Analysis 54 Journal of Theoretical Probability 52 Communications in Statistics. Theory and Methods 51 The Annals of Probability 50 Probability Theory and Related Fields 38 Bernoulli 34 The Annals of Applied Probability 31 Annals of the Institute of Statistical Mathematics 29 Journal of Mathematical Physics 29 Journal of Statistical Physics 29 Statistical Papers 29 Electronic Journal of Statistics 28 Journal of Statistical Computation and Simulation 22 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 21 Stochastic Processes and their Applications 19 Communications in Mathematical Physics 18 Journal of Econometrics 18 Statistics 16 Advances in Applied Probability 16 Computational Statistics 15 Metrika 15 Electronic Journal of Probability 15 Journal of Inequalities and Applications 15 Science China. Mathematics 14 Science in China. Series A 14 Test 14 Journal of the Korean Statistical Society 13 Acta Mathematicae Applicatae Sinica. English Series 12 Advances in Mathematics 12 Journal of Applied Probability 12 Acta Mathematica Sinica. English Series 11 Journal of Mathematical Analysis and Applications 11 Journal of the American Statistical Association 11 Journal of Functional Analysis 11 Linear Algebra and its Applications 11 Statistica Sinica 11 Journal of Nonparametric Statistics 11 Australian & New Zealand Journal of Statistics 10 Communications in Statistics. Simulation and Computation 9 Journal of Machine Learning Research (JMLR) 8 Scandinavian Journal of Statistics 8 Theory of Probability and its Applications 8 Journal of Mathematical Sciences (New York) 7 Biometrics 7 Random Structures & Algorithms 7 Journal of Applied Statistics 6 Communications on Pure and Applied Mathematics 6 Sequential Analysis 6 Statistical Science 6 Methodology and Computing in Applied Probability 6 Statistical Methodology 6 Journal of Statistical Theory and Practice 6 Sankhyā. Series A 5 Transactions of the American Mathematical Society 5 Journal of Time Series Analysis 5 European Journal of Operational Research 5 Applied Mathematics. Series B (English Edition) 5 Filomat 5 Mathematical Problems in Engineering 5 Annales Henri Poincaré 5 Brazilian Journal of Probability and Statistics 5 Journal of Systems Science and Complexity 5 Comptes Rendus. Mathématique. Académie des Sciences, Paris 5 AStA. Advances in Statistical Analysis 5 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 4 The Canadian Journal of Statistics 4 Indian Journal of Pure & Applied Mathematics 4 Israel Journal of Mathematics 4 Lithuanian Mathematical Journal 4 Proceedings of the American Mathematical Society 4 Geometric and Functional Analysis. GAFA 4 Abstract and Applied Analysis 4 Journal of the Royal Statistical Society. Series B. Statistical Methodology 4 Discrete Dynamics in Nature and Society 4 Journal of Applied Mathematics 4 ALEA. Latin American Journal of Probability and Mathematical Statistics 4 The Annals of Applied Statistics 3 Acta Mathematica Hungarica 3 Bulletin of the American Mathematical Society. New Series 3 Applied and Computational Harmonic Analysis 3 Mathematical Methods of Statistics 3 Combinatorics, Probability and Computing 3 Electronic Communications in Probability 3 Doklady Mathematics 3 Statistical Inference for Stochastic Processes 3 Journal of the European Mathematical Society (JEMS) 3 Econometric Theory 3 Quantitative Finance 3 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 3 Hacettepe Journal of Mathematics and Statistics 3 Statistical Methods and Applications 3 Oberwolfach Reports 3 Journal of Physics A: Mathematical and Theoretical 3 Journal of Mathematical Inequalities 3 Probability Surveys ...and 174 more Serials
all top 5

### Cited in 46 Fields

 1,224 Statistics (62-XX) 940 Probability theory and stochastic processes (60-XX) 477 Linear and multilinear algebra; matrix theory (15-XX) 144 Numerical analysis (65-XX) 79 Combinatorics (05-XX) 71 Functional analysis (46-XX) 71 Statistical mechanics, structure of matter (82-XX) 42 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 40 Computer science (68-XX) 31 Information and communication theory, circuits (94-XX) 30 Quantum theory (81-XX) 29 Operator theory (47-XX) 28 Biology and other natural sciences (92-XX) 23 Operations research, mathematical programming (90-XX) 14 Dynamical systems and ergodic theory (37-XX) 12 Convex and discrete geometry (52-XX) 12 Systems theory; control (93-XX) 11 Special functions (33-XX) 9 Approximations and expansions (41-XX) 7 Number theory (11-XX) 7 Ordinary differential equations (34-XX) 7 Partial differential equations (35-XX) 7 Harmonic analysis on Euclidean spaces (42-XX) 6 History and biography (01-XX) 5 General and overarching topics; collections (00-XX) 5 Integral transforms, operational calculus (44-XX) 4 Group theory and generalizations (20-XX) 4 Functions of a complex variable (30-XX) 3 Real functions (26-XX) 3 Global analysis, analysis on manifolds (58-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Geometry (51-XX) 2 General topology (54-XX) 2 Fluid mechanics (76-XX) 2 Classical thermodynamics, heat transfer (80-XX) 2 Relativity and gravitational theory (83-XX) 2 Astronomy and astrophysics (85-XX) 2 Geophysics (86-XX) 1 Nonassociative rings and algebras (17-XX) 1 Topological groups, Lie groups (22-XX) 1 Measure and integration (28-XX) 1 Potential theory (31-XX) 1 Difference and functional equations (39-XX) 1 Abstract harmonic analysis (43-XX) 1 Integral equations (45-XX) 1 Differential geometry (53-XX)