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.
Funding agency
This research is supported by the Thematic Research Agency in Science and Technology (ATRST-Algeria).
Received: 08.04.2020 Received in revised form: 01.06.2020 Accepted: 16.07.2020
Bibliographic databases:
Document Type:
Article
UDC:
517.9
Language: English
Citation:
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., 13:5 (2020), 608–621
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\by Abdenour~Hamdaoui, Abdelkader~Benkhaled, Mekki~Terbeche
\paper Baranchick-type estimators of a multivariate normal mean under the general quadratic loss function
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2020
\vol 13
\issue 5
\pages 608--621
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\crossref{https://doi.org/10.17516/1997-1397-2020-13-5-608-621}
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Linking options:
https://www.mathnet.ru/eng/jsfu867
https://www.mathnet.ru/eng/jsfu/v13/i5/p608
This publication is cited in the following 2 articles:
Abdelkader Benkhaled, Abdenour Hamdaoui, Waleed Almutiry, Mohammed Alshahrani, Mekki Terbeche, “A study of minimax shrinkage estimators dominating the James-Stein estimator under the balanced loss function”, Open Mathematics, 20:1 (2022), 1
Abdenour Hamdaoui, “On shrinkage estimators improving the positive part of James-Stein estimator”, Demonstratio Mathematica, 54:1 (2021), 462
Citation in format AMSBIB
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