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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
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.
Received: 30.06.2021
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
Linking options:
https://www.mathnet.ru/eng/emj435 https://www.mathnet.ru/eng/emj/v13/i2/p18
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Abstract page: | 94 | Full-text PDF : | 78 | References: | 9 |
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