Polynomials Shrinkage Estimators of a Multivariate Normal Mean

  • Abdelkader Benkhaled Mascara University, Algeria
  • Mekki Terbeche Algeria
  • Abdenour Hamdaoui University of Sciences and Technologies Mohamed Boudiaf, Oran (USTO).Department of Mathematics. Algeria
Keywords: Balanced Loss Function, James-Stein estimator, multivariate Gaussian random variable, non-central chi-square distribution, shrinkage estimators.


In this work, the estimation of the multivariate normal mean by different classes of shrinkage estimators is investigated. The risk associated with the balanced loss function is used to compare two estimators. We start by considering estimators that generalize the James-Stein estimator and show that these estimators dominate the maximum likelihood estimator (MLE), therefore are minimax, when the shrinkage function satisfifies some conditions. Then, we treat estimators of polynomial form and prove the increase of the degree of the polynomial allows us to build a better estimator from the one previously constructed.

Author Biography

Abdenour Hamdaoui, University of Sciences and Technologies Mohamed Boudiaf, Oran (USTO).Department of Mathematics. Algeria
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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How to Cite
Benkhaled, A., Terbeche, M., & Hamdaoui, A. (2021). Polynomials Shrinkage Estimators of a Multivariate Normal Mean. Statistics, Optimization & Information Computing, 10(2), 572-588. https://doi.org/10.19139/soic-2310-5070-1095
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