Xu, Xiaoming; Meyer, Mary C.; Opsomer, Jean D. Improved variance estimation for inequality-constrained domain mean estimators using survey data. (English) Zbl 1477.62084 J. Stat. Plann. Inference 215, 47-71 (2021). Summary: In survey domain estimation, a priori information can often be imposed in the form of linear inequality constraints on the domain estimators. J. Wu et al. [Can. J. Stat. 44, No. 4, 431–444 (2016; Zbl 1357.62056)] formulated the isotonic domain mean estimator, for the simple order restriction, and methods for more general constraints were proposed in C. Oliva-Avilés et al. [“Estimation and inference of domain means subject to qualitative constraints”, Surv. Methodol. 46, No. 2, 145–180 (2020)]. When the assumptions are valid, imposing restrictions on the estimators will ensure that the a priori information is respected, and in addition allows information to be pooled across domains, resulting in estimators with smaller variance. Here, we propose a method to further improve the estimation of the covariance matrix for these constrained domain estimators, using a mixture of possible covariance matrices obtained from the inequality constraints. We prove consistency of the improved variance estimator, and simulations demonstrate that the new estimator results in improved coverage probabilities for domain mean confidence intervals, while retaining the smaller confidence interval lengths. MSC: 62G05 Nonparametric estimation 62G08 Nonparametric regression and quantile regression 62G15 Nonparametric tolerance and confidence regions 62H12 Estimation in multivariate analysis 62D05 Sampling theory, sample surveys 62D20 Causal inference from observational studies 60E15 Inequalities; stochastic orderings Keywords:covariance estimation; confidence intervals; survey domain Citations:Zbl 1357.62056 Software:coneproj PDFBibTeX XMLCite \textit{X. Xu} et al., J. Stat. Plann. Inference 215, 47--71 (2021; Zbl 1477.62084) Full Text: DOI References: [1] Boistard, H.; Lopuhaa, H. P.; Ruiz-Gazen, A., Approximation of rejective sampling inclusion probabilities and application to high order correlations, Electron. J. Stat., 6, 1967-1983 (2012) · Zbl 1295.62009 [2] Breidt, F.; Opsomer, J., Local polynomial regression estimators in survey sampling, Ann. Statist., 28, 4, 1026-1053 (2000) · Zbl 1105.62302 [3] Breidt, F. J.; Opsomer, J. D., Model-assisted survey estimation with modern prediction techniques, Statist. Sci., 32, 2, 190-205 (2017) · Zbl 1381.62060 [4] Hájek, J., Asymptotic theory of rejective sampling with varying probabilities from a finite population, Ann. Math. Stat., 35, 1491-1523 (1964) · Zbl 0138.13303 [5] Hájek, J., Comment on a paper by D. Basu, (Godambe, V. P.; Sprott, D. A., Foundations of Statistical Inference (1971), Holt, Rinehart and Winston: Holt, Rinehart and Winston Toronto), 236 [6] Horvitz, D. G.; Thompson, D. J., A generalization of sampling without replacement from a finite universe, J. Amer. Statist. Assoc., 47, 663-685 (1952) · Zbl 0047.38301 [7] Liao, X.; Meyer, M. C., Coneproj: an r package for the primal or dual cone projections with routines for constrained regression, J. Stat. Softw., 61, 1-22 (2014) [8] Meyer, M. C., An extension of the mixed primal-dual bases algorithm to the case of more constraints than dimensions, J. Statist. Plann. Inference, 81, 13-31 (1999) · Zbl 1057.62510 [9] Oliva-Avilés, C.; Meyer, M. C.; Opsomer, J. D., Checking validity of monotone domain mean estimators, Canad. J. Statist., 47, 2, 315-331 (2019) · Zbl 1522.62008 [10] Oliva-Avilés, C.; Opsomer, J. D.; Meyer, M. C., Estimation and inference of domain means subject to qualitative constraints, Surv. Methol., accepted (2020) [11] Robertson, T.; Wright, F. T.; Dykstra, R. L., Order Restricted Statistical Inference (1988), John Wiley & Sons: John Wiley & Sons New York · Zbl 0645.62028 [12] Silvapulle, M. J.; Sen, P., Constrained Statistical Inference (2005), Wiley: Wiley Hoboken, New Jersey · Zbl 1077.62019 [13] Wu, J.; Meyer, M. C.; Opsomer, J. D., Survey estimation of domain means that respect natural orderings, Canad. J. Statist., 44, 4, 431-444 (2016) · Zbl 1357.62056 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.