Journal of Siberian Federal University. Mathematics & Physics / Limits of Risks Ratios of Shrinkage Estimators under the Balanced Loss Function

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Issue
Journal of Siberian Federal University. Mathematics & Physics. 2021 14 (3)
Authors
Terbeche, Mekki; Benkhaled, Abdelkader; Hamdaoui, Abdenour
Contact information
Terbeche, Mekki: University of Sciences and Technology, Mohamed Boudiaf, Oran Laboratory of Analysis and Application of Radiation (LAAR), USTO-MB Oran, Algeria; ; Benkhaled, Abdelkader: Mascara University, Mustapha Stambouli Laboratory of Geomatics, Ecology and Environment (LGEO2E), Mascara University Mascara, Algeria; ; Hamdaoui, Abdenour: University of Sciences and Technology, Mohamed Boudiaf, Oran Laboratory of Statistics and Random Modelisations (LSMA) of Tlemcen University Oran, Algeria; ;
Keywords
balanced Loss Function; James-Stein estimator; multivariate Gaussian random variable; non-central chi-square distribution; shrinkage estimators
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

Pages
301–312
DOI
10.17516/1997-1397-2021-14-3-301-312
Paper at repository of SibFU
https://elib.sfu-kras.ru/handle/2311/140060