ORIGINAL RESEARCH article
Front. Appl. Math. Stat.
Sec. Statistics and Probability
A new approach for shrinkage estimators of the multivariate normal mean vector under the balanced loss criterion
Provisionally accepted
- 1Qassim University, Buraydah, Saudi Arabia
- 2University of science and technology USTOMB, Oran, Algeria
- 3Universite Mustapha Stambouli Mascara, Mascara, Algeria
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In this paper, we investigate the problem of estimating the mean vector of a mul-tivariate normal distribution. We introduce two new families of shrinkage estima-tors which derived from both the maximum likelihood estimator and the James-Stein estimator. To evaluate their performance, we employ the risk function corresponding to the balanced loss function. Using that criterion, we establish that these estimators consistently outperform the positive-part of James-Stein estimator. Furthermore, we show that the estimators from the second family exhibit better performance than those from the first. Finally, we conclude with simulation studies that confirm our theoretical findings.
Keywords: balanced loss function, Multivariate normal distribution, positive part of James-Stein estimator, Risk function, Shrinkage estimator
Received: 21 Sep 2025; Accepted: 29 Nov 2025.
Copyright: © 2025 M. ALoraini, Hamdaoui and Benkhaled. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
* Correspondence:
Najla M. ALoraini
Abdenour Hamdaoui
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