On the effectiveness of the new estimators obtained from the Bayes estimator

Amani Alahmadi; Abdelkader Benkhaled; Waleed Almutiry; Amani Alahmadi; Abdelkader Benkhaled; Waleed Almutiry

doi:10.3934/math.2025265

AIMS Mathematics

2025, Volume 10, Issue 3: 5762-5784. doi: 10.3934/math.2025265

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Research article

On the effectiveness of the new estimators obtained from the Bayes estimator

1.
Department of Mathematics, College of Science and Humanities in Ad Dawadmi, Shaqra University, Shaqra, Saudi Arabia; Email: aalahmadi@su.edu.sa
2.
Department of Biology, University of Mascara, Laboratory of Stochastic Models, Statistics and Applications, University Tahar Moulay of Saïda, Mascara, Algeria; Email: benkhaled08@yahoo.fr
3.
Department of Mathematics, College of Science and Art in Ar Rass, Qassim University, Saudi Arabia; Email: wkmtierie@qu.edu.sa

Received: 13 September 2024 Revised: 18 February 2025 Accepted: 26 February 2025 Published: 14 March 2025
MSC : 60E05, 62H10

Estimating the mean parameters in random variables, particularly within multivariate normal distributions, is a critical issue in statistics. Traditional methods, such as the maximum likelihood estimator, often struggle in high-dimensional or small-sample contexts, driving interest in shrinkage estimators that enhance accuracy by reducing variance. This study builds on the foundational work by Stein and others examining the minimax properties of shrinkage estimators. In this paper, we propose Bayesian estimation techniques that incorporate prior information within a balanced loss function framework, aiming to improve upon existing methods. Our findings demonstrate the advantages of using the balanced loss function for performance evaluation, which offers a robust alternative to conventional quadratic loss functions. In this paper, we present the theoretical foundations, a simulation study, and an application to real data.
- minimax estimator,
- balanced loss function,
- James-Stein,
- multivariate Gaussian random variable estimator,
- shrinkage estimators,
- non-central chi-square distribution
Citation: Amani Alahmadi, Abdelkader Benkhaled, Waleed Almutiry. On the effectiveness of the new estimators obtained from the Bayes estimator[J]. AIMS Mathematics, 2025, 10(3): 5762-5784. doi: 10.3934/math.2025265

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Abstract

Estimating the mean parameters in random variables, particularly within multivariate normal distributions, is a critical issue in statistics. Traditional methods, such as the maximum likelihood estimator, often struggle in high-dimensional or small-sample contexts, driving interest in shrinkage estimators that enhance accuracy by reducing variance. This study builds on the foundational work by Stein and others examining the minimax properties of shrinkage estimators. In this paper, we propose Bayesian estimation techniques that incorporate prior information within a balanced loss function framework, aiming to improve upon existing methods. Our findings demonstrate the advantages of using the balanced loss function for performance evaluation, which offers a robust alternative to conventional quadratic loss functions. In this paper, we present the theoretical foundations, a simulation study, and an application to real data.

References

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