A NEW CLASS OF MINIMAX ESTIMATORS OF MULTIVARIATE NORMAL MEAN VECTORS UNDER BALANCED LOSS FUNCTION

1999 ◽  
Vol 17 (3) ◽  
Author(s):  
Dipak K. Dey ◽  
Chansoo Kim ◽  
Younshik Chung
Keyword(s):  
Loss Function ◽  
Multivariate Normal ◽  
Balanced Loss Function ◽  
New Class ◽  
Multivariate Normal Mean ◽  
Minimax Estimators ◽  
Normal Mean ◽  
Mean Vectors

scholarly journals Limits of Risks Ratios of Shrinkage Estimators under the Balanced Loss Function

2021 ◽  
pp. 301-312
Author(s):  
Mekki Terbeche
Keyword(s):  
Maximum Likelihood ◽  
Loss Function ◽  
Sufficient Conditions ◽  
Maximum Likelihood Estimators ◽  
Shrinkage Estimators ◽  
Multivariate Normal ◽  
Balanced Loss Function ◽  
Multivariate Normal Mean ◽  
Normal Mean ◽  
Stein Estimator

In this paper we study the estimation of a multivariate normal mean under the balanced loss function. We present here a class of shrinkage estimators which generalizes the James-Stein estimator and we are interested to establish the asymptotic behaviour of risks ratios of these estimators to the maximum likelihood estimators (MLE). Thus, in the case where the dimension of the parameter space and the sample size are large, we determine the sufficient conditions for that the estimators cited previously are minimax

scholarly journals On shrinkage estimators improving the James-Stein estimator under balanced loss function

2021 ◽  
pp. 711-727
Author(s):  
Abdenour Hamdaoui ◽  
Mekki Terbeche ◽  
Abdelkader Benkhaled
Keyword(s):  
Maximum Likelihood ◽  
Loss Function ◽  
Shrinkage Estimators ◽  
Multivariate Normal ◽  
Likelihood Estimator ◽  
Balanced Loss Function ◽  
Multivariate Normal Mean ◽  
Normal Mean ◽  
Stein Estimator ◽  
Class Of Estimators

In this paper, we are interested in estimating a multivariate normal mean under the balanced loss function using the shrinkage estimators deduced from the Maximum Likelihood Estimator (MLE). First, we consider a class of estimators containing the James-Stein estimator, we then show that any estimator of this class dominates the MLE, consequently it is minimax. Secondly, we deal with shrinkage estimators which are not only minimax but also dominate the James- Stein estimator.

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