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Eurasian Mathematical Journal, 2022, Volume 13, Number 2, Pages 18–36
DOI: https://doi.org/10.32523/2077-9879-2022-13-2-18-36 (Mi emj435) 		 
Minimax shrinkage estimators and estimators dominating the James-Stein estimator under the balanced loss function

A. Benkhaledab, A. Hamdaouicd, M. Terbecheed

a Department of Biology, Mascara University, Mascara, Algerie
b Laboratory of Stochastic Models, Statistics and Applications, University Tahar Moulay of Saida, Bp 305, Route de Mamounia 29000, Mascara, Algerie
c Laboratory of Statistics and Random Modelisations of University Abou Bekr Belkaid (LSMA), Tlemcen, El Mnaouar, BP 1505, Bir El Djir 31000, Oran, Algeria
d Department of Mathematics, University of Sciences and Technology, Mohamed Boudiaf, Oran
e Laboratory of Analysis and Application of Radiation (LAAR), USTO-MB, El Mnaouar, BP 1505, Bir El Djir 31000, Oran, Algeria
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DOI: https://doi.org/10.32523/2077-9879-2022-13-2-18-36
Abstract: This paper is dealing with the shrinkage estimators of a multivariate normal mean and their minimaxity properties under the balanced loss function. We present here two different classes of estimators: the first which generalizes the James-Stein estimator, and show that any estimator of this class dominates the maximum likelihood estimator (MLE), consequently it is minimax, and the second dominates the James-Stein estimator and we conclude that any estimator of this class is also minimax.
Keywords and phrases: Balanced loss function, James-Stein estimator, minimax estimator, multivariate Gaussian random variable, non-central chi-square distribution, shrinkage estimators.
Funding agency Grant number
Directorate-General for Scientific Research and Technological Development
This research was partially supported by the DGRSDT-MESRS-Algeria.
Received: 30.06.2021
Bibliographic databases:
Document Type: Article
MSC: Primary 62C20; Secondary 62H10, 62J07
Language: English
Citation: A. Benkhaled, A. Hamdaoui, M. Terbeche, “Minimax shrinkage estimators and estimators dominating the James-Stein estimator under the balanced loss function”, Eurasian Math. J., 13:2 (2022), 18–36
Citation in format AMSBIB
\Bibitem{BenHamTer22}
\by A.~Benkhaled, A.~Hamdaoui, M.~Terbeche
\paper Minimax shrinkage estimators and estimators dominating the James-Stein estimator under the balanced loss function
\jour Eurasian Math. J.
\yr 2022
\vol 13
\issue 2
\pages 18--36
\mathnet{http://mi.mathnet.ru/emj435}
\crossref{https://doi.org/10.32523/2077-9879-2022-13-2-18-36}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4459172}
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