MSE performance of the weighted average estimators consisting of shrinkage estimators

ABSTRACT

In this paper, we consider a regression model and propose estimators which are the weighted averages of two estimators among three estimators; the Stein-rule (SR), the minimum mean squared error (MMSE), and the adjusted minimum mean-squared error (AMMSE) estimators. It is shown that one of the proposed estimators has smaller mean-squared error (MSE) than the positive-part Stein-rule (PSR) estimator over a moderate region of parameter space when the number of the regression coefficients is small (i.e., 3), and its MSE performance is comparable to the PSR estimator even when the number of the regression coefficients is not so small.

KEYWORDS:

• Adjusted minimum mean-squared error estimator
• mean-squared error
• minimum-mean squared error estimator
• Stein-rule estimator
• weighted average estimator

MATHEMATICS SUBJECT CLASSIFICATION:

• 62J07
• 62J05

Acknowledgment

The authors are grateful for anonymous referees for helpful comments and suggestions.

Funding

This work was supported by JSPS KAKENHI grant numbers 23243038, 26780136.

Notes

1 As is suggested by an anonymous referee, we also calculated the squared lengths of bias of the estimators under the simplified assumptions. See Appendix B for details.