Asymptotic risk behavior of mean vector and variance estimators and the problem of positive normal mean

DOI10.1007/BF00058642zbMath0781.62071MaRDI QIDQ1206654

Andrew. L. Rukhin

Publication date: 1 April 1993

Published in: Annals of the Institute of Statistical Mathematics (Search for Journal in Brave)

zbMATH Keywords

multivariate normal distributionunknown variancerelative risk reductionunknown meanasymptotic risk behaviorbowl-shaped loss functionBrewster-Zidek variance estimator of the normal variancegeneral lossJames-Stein estimator of normal meanpositive normal mean under quadratic lossscale-equivariant estimatorsStein estimator of normal variance

Mathematics Subject Classification ID

Asymptotic properties of parametric estimators (62F12) Estimation in multivariate analysis (62H12) Admissibility in statistical decision theory (62C15)

Related Items (4)

Decision-theoretic issues in heterogeneity variance estimation ⋮ General dominance properties of double shrinkage estimators for ratio of positive parameters ⋮ Influence of the prior distribution on the risk of the Bayes rule ⋮ Shrinkage and modification techniques in estimation of variance and the related problems: A review

Cites Work

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• Asymptotic risk comparison of improved estimators for normal covariance matrix
• Risk behavior of variance estimators in multivariate normal distribution
• Families of minimax estimators of the mean of a multivariate normal distribution
• Developments in decision-theoretic variance estimation. With comments and a rejoinder by the authors
• Improving on equivariant estimators
• Inadmissibility of the usual estimator for the variance of a normal distribution with unknown mean
• Limit expressions for the risk of james‐stein estimators
• Admissible and Minimax Estimates of Parameters in Truncated Spaces

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