On a Comparison of Several Competing Estimates of a Univariate Normal Mean by the Multiple Criteria Decision-Making Method

Abstract

In this article we consider the problem of estimation of the mean of a univariate normal population with an unknown variance when uncertain nonsample prior information about the mean is available. We compare four estimators of the mean, including pretest and shrinkage estimators. The performances of the estimators are compared based on the multiple criteria decision making (MCDM) procedure in order to find the best estimator.

Keywords:

• Multiple criteria decision making
• Pretest estimate
• Shrinkage estimate
• Univariate normal mean

AMS 2000 Subject Classification:

• 62C25
• 62G05

Acknowledgments

We are extremely thankful to a referee for some helpful comments that improved the presentation. We also thank the Thailand Research Fund and the Commission on Higher Education for the financial support.

Notes

F _1,4;.05 = 7.7086, F _1,9;.05 = 5.1173, F _1,14;.05 = 4.6001.

F _1,4;.25 = 1.8074, F _1,9;.25 = 1.5121, F _1,14;.25 = 1.4403.

F _1,4;.5 = 0.5486, F _1,9;.5 = 0.4938, F _1,14;.5 = 0.4794.

*Rank 1 = best, rank 3 = worst.

*Rank 1 = best, rank 3 = worst.

*Rank 1 = best, rank 3 = worst.