On shrinkage estimators improving the positive part of James-Stein estimator

Demonstratio Mathematica

Hamdaoui Abdenour¹ 

[1] Department of Mathematics, University of Sciences and Technology, Mohamed Boudiaf, Oran, Laboratory of Statistics and Random Modelisations of Tlemcen University (LSMA), Algeria;

关键词: james-stein estimator;    multivariate normal distribution;    non-central chi-square distribution;    quadratic loss function;    shrinkage estimators;    62j07;    62c20;    62h10;   

DOI  :  10.1515/dema-2021-0038

来源: DOAJ

【 摘 要 】

In this work, we study the estimation of the multivariate normal mean by different classes of shrinkage estimators. The risk associated with the quadratic loss function is used to compare two estimators. We start by considering a class of estimators that dominate the positive part of James-Stein estimator. Then, we treat estimators of polynomial form and prove if we increase the degree of the polynomial we can build a better estimator from the one previously constructed. Furthermore, we discuss the minimaxity property of the considered estimators.

【 授权许可】

Unknown