Sankhya: The Indian Journal of Statistics

1993, Volume 55, Series A, Pt. 2, 285--304

EMPIRICAL BAYES ESTIMATION FOR THE MEANS OF THE SELECTED POPULATIONS

By

JIUNN T. HWANG, Cornell University

 

SUMMARY. The problem of estimation after selection can arise in many statistical applications. The intuitive estimator constructed as if there were no prior selection appears to be misleading. This is especially so when one is estimating the characteristic of the chosen population, selected to maximise estimates of the similar characteristics. In such a case, the intuitive estimator highly overestimate the chosen characteristic. The characteristic focussed here is the mean and a normal parametric assumption of the observations is made. The problem of improving upon the intuitive estimators appears to be technically very difficult. No alternative estimator has been proposed which was shown to dominate the intuitive estimator in any sense. We provide an empirical Bayes estimator which was shown to dominate the intuitive estimator in terms of Bayes risk with respect to any normal prior. Note that the frequentist risk domination is not possible. Numerical studies also provide strong evidence that the domination is robust with respect to independently identically distributed priors, not necessarily normal. the estimator does not overestimate the target parameter for many circumstances.

 

AMS (1990) subject classification. 62F15,62C12, 62F10

Key words and phrases. Estimation after selection, bias, risk, Lindley's estimator

FULL PAPER.

This article in Mathematical Reviews.