An adaptive empirical Bayes estimator of the multivariate normal mean under quadratic loss

1990 ◽  
Vol 44 (1-2) ◽  
pp. 189-213 ◽  
Author(s):  
G.G. Judge ◽  
R.Carter Hill ◽  
M.E. Bock
Keyword(s):  
Empirical Bayes ◽  
Bayes Estimator ◽  
Quadratic Loss ◽  
Multivariate Normal ◽  
Multivariate Normal Mean ◽  
Normal Mean ◽  
Empirical Bayes Estimator

scholarly journals Baranchick-type Estimators of a Multivariate Normal Mean Under the General Quadratic Loss Function

2020 ◽  
pp. 608-621
Author(s):  
Abdenour Hamdaoui ◽  
Abdelkader Benkhaled ◽  
Mekki Terbeche
Keyword(s):  
Loss Function ◽  
General Situation ◽  
Quadratic Loss ◽  
Shrinkage Estimators ◽  
Multivariate Normal ◽  
Multivariate Normal Mean ◽  
The Matrix ◽  
Normal Mean ◽  
Stein Estimator ◽  
The Mean

The problem of estimating the mean of a multivariate normal distribution by different types of shrinkage estimators is investigated. We established the minimaxity of Baranchick-type estimators for identity covariance matrix and the matrix associated to the loss function is diagonal. In particular the class of James-Stein estimator is presented. The general situation for both matrices cited above is discussed

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

2021 ◽  
Vol 54 (1) ◽  
pp. 462-473
Author(s):  
Abdenour Hamdaoui
Keyword(s):  
Loss Function ◽  
Quadratic Loss ◽  
Shrinkage Estimators ◽  
Multivariate Normal ◽  
Positive Part ◽  
Multivariate Normal Mean ◽  
Normal Mean ◽  
Stein Estimator ◽  
Class Of Estimators ◽  
The One

Abstract 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.

scholarly journals Admissible estimators of a multivariate normal mean vector when the scale is unknown

Biometrika ◽  
2020 ◽  
Author(s):  
Y Maruyama ◽  
W E Strawderman
Keyword(s):  
Normal Vector ◽  
Quadratic Loss ◽  
Multivariate Normal ◽  
Bayes Estimators ◽  
Multivariate Normal Mean ◽  
Generalized Bayes ◽  
Normal Mean ◽  
Mean Vector

Abstract We study admissibility of a subclass of generalized Bayes estimators of a multivariate normal vector when the variance is unknown, under scaled quadratic loss. Minimaxity is established for some of these estimators.

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