An improvement of James-Stein estimator under the balanced loss function†
In Bong Choi1 · Hoh Yoo Baek2 · Jeong Mi Lee3
1Korea Institute For Curriculum and Evaluation
2Division of Big Data and Financial Statistics, Wonkwang University
3Department of Public Health, Wonkwang University Graduate School
2Division of Big Data and Financial Statistics, Wonkwang University
3Department of Public Health, Wonkwang University Graduate School
Correspondence to: † This research was supported by Wonkwang University in 2023.
1 Research commissioner, Korea Institute For Curriculum and Evaluation, Jincheon 27873, Korea.
2 Professor emeritus, Division of Big Data and Financial Statistics,, Wonkwang University, Iksan 54538, Korea.
3 Corresponding author: Associate professor, Department of Public Health, Wonkwang University Graduate School, Iksan 54538, Korea. E-mail: aura-lee@hanmail.net
1 Research commissioner, Korea Institute For Curriculum and Evaluation, Jincheon 27873, Korea.
2 Professor emeritus, Division of Big Data and Financial Statistics,, Wonkwang University, Iksan 54538, Korea.
3 Corresponding author: Associate professor, Department of Public Health, Wonkwang University Graduate School, Iksan 54538, Korea. E-mail: aura-lee@hanmail.net
Received August 3, 2023; Revised August 31, 2023; Accepted September 1, 2023.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
- Abstract
- In this paper we are dealing with the shrinkage estimators of a multivariate normal mean and their minimaxity properties under the balanced loss function. This paper is presented here two different classes of estimator. First, we generalize the James-Stein estimator and show that any estimator of this class dominates the usual estimator. Second, we can also show that it dominates the James-Stein estimator and conclude that any estimator of this class is minimax.
- Keywords : Balanced loss function, James-Stein estimator, minimax estimator, multivariate normal mean, shrinkage estimator
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