On Performance of Competing Estimators Under Bayes, Frequentist, and Combined Frameworks

SYNOPTIC ABSTRACT

In the present article, a confidence interval based on a combined estimator, a fusion of Bayes and frequentist estimators, is proposed. An evaluation has been done to compare it with the competing confidence intervals based on best frequentist estimator and Bayes estimator. The condition for the combined estimator to outperform the best frequentist estimator under true prior has been derived. The performance of the confidence interval based on the proposed combined estimator has been found to supersede the performance of the other competing estimators when comparison is made in terms of coverage probability or coverage probability per mean width. It has been observed that the superiority of one estimator over the other depends on the quality of the prior information. A Poisson experiment has been conducted to generate the data, on the basis of which a rigorous simulation study has been performed to reach a decision about the superiority of the proposed estimator.

Key Words and Phrases::

• Bayes estimator
• confidence interval estimator
• coverage probability per mean width
• frequentist estimator
• LINEX risk

Acknowledgment

The authors are grateful to Professor F. J. Samaniego of the Department of Statistics, University of California, Davis, for posing the problem and giving insight into it.