Polynomials Shrinkage Estimators of a Multivariate Normal Mean

Statistics, Optimization and Information Computing

article

Abdelkader Benkhaled¹  Mekki Terbeche²  Abdenour Hamdaoui³ 

[1] Mascara University;Algeria;University of Sciences and Technologies Mohamed Boudiaf, Oran ,(USTO).Department of Mathematics. Algeria

关键词: Balanced Loss Function;    James-Stein estimator;    multivariate Gaussian random variable;    non-central chi-square distribution;    shrinkage estimators.;   

DOI  :  10.19139/soic-2310-5070-1095

来源: Istituto Superiore di Sanita

【 摘 要 】

In this work, the estimation of the multivariate normal mean by different classes of shrinkage estimators is investigated. The risk associated with the balanced loss function is used to compare two estimators. We start by considering estimators that generalize the James-Stein estimator and show that these estimators dominate the maximum likelihood estimator (MLE), therefore are minimax, when the shrinkage function satisfifies some conditions. Then, we treat estimators of polynomial form and prove the increase of the degree of the polynomial allows us to build a better estimator from the one previously constructed.

【 授权许可】

Unknown