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.

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.

SHRINKAGE EFFICIENCY BOUNDS

2014 ◽  
Vol 31 (4) ◽  
pp. 860-879 ◽  
Author(s):  
Bruce E. Hansen
Keyword(s):  
Sufficient Conditions ◽  
Shrinkage Estimation ◽  
Shrinkage Estimators ◽  
Multivariate Normal ◽  
Squared Error ◽  
Multiple Dimensions ◽  
Multivariate Normal Mean ◽  
Normal Mean ◽  
Lower Maximum ◽  
Maximum Regret

This paper is an extension of Magnus (2002, Econometrics Journal 5, 225–236) to multiple dimensions. We consider estimation of a multivariate normal mean under sum of squared error loss. We construct the efficiency bound (the lowest achievable risk) for minimax shrinkage estimation in the class of minimax orthogonally invariate estimators satisfying the sufficient conditions of Efron and Morris (1976, Annals of Statistics 4, 11–21). This allows us to compare the regret of existing orthogonally invariate shrinkage estimators. We also construct a new shrinkage estimator which achieves substantially lower maximum regret than existing estimators.

scholarly journals Minimaxity and Limits of Risks Ratios of Shrinkage Estimators of a Multivariate Normal Mean in the Bayesian Case

2020 ◽  
Vol 8 (2) ◽  
pp. 507-520
Author(s):  
Abdenour Hamdaoui ◽  
Abdelkader Benkhaled ◽  
Nadia Mezouar
Keyword(s):  
Maximum Likelihood ◽  
Sample Size ◽  
Maximum Likelihood Estimator ◽  
Bayes Estimator ◽  
Shrinkage Estimators ◽  
Multivariate Normal ◽  
Likelihood Estimator ◽  
Unknown Variance ◽  
Multivariate Normal Mean ◽  
Normal Mean

In this article, we consider two forms of shrinkage estimators of a multivariate normal mean with unknown variance. We take the prior law as a normal multivariate distribution and we construct a Modified Bayes estimator and an Empirical Modified Bayes estimator. We are interested instudying the minimaxity and the behavior of risks ratios of these estimators to the maximum likelihood estimator, when the dimension of the parameters space and the sample size tend to infinity.

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