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

  • Abdenour Hamdaoui University of Sciences and Technologies Mohamed Boudiaf, Oran (USTO). Department of Mathematics.
  • Abdelkader Benkhaled Department of Biology, Mascara University, Algeria
  • Nadia Mezouar Faculty of Economics and Commercial Sciences, Mascara University
DOI: https://doi.org/10.19139/soic-2310-5070-735
Keywords: Bayes estimator, James-Stein estimator, Modified Bayes estimator, Multivariate Gaussian random variable, Quadratic risk, Shrinkage estimator.

Abstract

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.

Author Biography

Abdenour Hamdaoui, University of Sciences and Technologies Mohamed Boudiaf, Oran (USTO). Department of Mathematics.
Doctorat in Mathematics (PhD) option of Probability and statistics at the Department of Mathematics, University of Tlemcen, Algeria.Senior lecturer at the Department of Mathematics, University of Science and Technology of Oran Mohamed Boudiaf (USTO-MB), Oran, Algeria.

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Published
2020-02-17
How to Cite
Hamdaoui, A., Benkhaled , A., & Mezouar, N. (2020). Minimaxity and Limits of Risks Ratios of Shrinkage Estimators of a Multivariate Normal Mean in the Bayesian Case. Statistics, Optimization & Information Computing, 8(2), 507-520. https://doi.org/10.19139/soic-2310-5070-735
Issue
Vol 8 No 2 (2020)
Section
Research Articles
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