Limits of risks ratios of shrinkage estimators under the balanced loss function

Mekki Terbeche^a, Abdelkader Benkhaled^b, Abdenour Hamdaoui<sup>a

a</sup> University of Sciences and Technology, Mohamed Boudiaf, Oran, Laboratory of Analysis and Application of Radiation (LAAR), USTO-MB, Oran, Algeria
^b Mascara University, Mustapha Stambouli, Laboratory of Geomatics, Ecology and Environment (LGEO2E), Mascara University, Mascara, Algeria

Abstract: 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.

Keywords: balanced Loss Function, James-Stein estimator, multivariate Gaussian random variable, non-central chi-square distribution, shrinkage estimators.

UDC: 519.2

Received: 10.12.2020
Received in revised form: 04.02.2021
Accepted: 02.03.2021

Language: English

DOI: 10.17516/1997-1397-2021-14-3-301-312

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