Abdenour Hamdaoui, Abdelkader Benkhaled, Mekki Terbeche, “Baranchick-type estimators of a multivariate normal mean under the general quadratic loss function”, J. Sib. Fed. Univ. Math. Phys., 2020, Volume 13, Issue 5,Pages <nobr>608

This article is cited in 2 papers

Baranchick-type estimators of a multivariate normal mean under the general quadratic loss function

Abdenour Hamdaoui^ab, Abdelkader Benkhaled^c, Mekki Terbeche^da

^a Department of Mathematics University of Sciences and Technology, Mohamed Boudiaf, Oran, Algeria
^b Laboratory of Statistics and Random Modelisations (LSMA), Tlemcen, Algeria
^c Department of Biology Mascara University Mustapha Stambouli, Laboratory of Geomatics, Ecology and Environment (LGEO2E), Mascara, Algeria
^d Laboratory of Analysis and Application of Radiation (LAAR), USTO-MB, Oran, Algeria

Abstract: The problem of estimating the mean of a multivariate normal distribution by different types of shrinkage estimators is investigated. We established the minimaxity of Baranchick-type estimators for identity covariance matrix and the matrix associated to the loss function is diagonal. In particular the class of James–Stein estimator is presented. The general situation for both matrices cited above is discussed.

Keywords: сovariance matrix, James–Stein estimator, loss function, multivariate gaussian random variable, non-central chi-square distribution, shrinkage estimator.

UDC: 517.9

Received: 08.04.2020
Received in revised form: 01.06.2020
Accepted: 16.07.2020

Language: English

DOI: 10.17516/1997-1397-2020-13-5-608-621