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An improvement of James-Stein estimator under the balanced loss function
Journal of the Korean Data & Information Science Society 2023;34:837-54
Published online September 30, 2023;
© 2023 Korean Data and Information Science Society.

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
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:
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 ( which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
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