Expansions of the coverage probabilities of prediction region based on a shrinkage estimator

Abstract

An expansion formula for the coverage probability of prediction region based on a shrinkage estimator proposed by Joshi [Joshi, V. M. (1967). Inadmissibility of the usual confidence sets for the mean of a multivariate normal population. Ann. Math. Statist., 38, 1868–1875.] is obtained. Its error bound is evaluated in terms of a function of an unknown parameter. Applying this result, three types of asymptotic expansions are derived. These expansions show inadmissibility of the usual prediction region.

Keywords:

• Asymptotic expansion
• Malliavin calculus
• Prediction region
• Inadmissibility

Notes

The method used in this article can be applied to the confidence region, and supplies another approach to the result of Joshi (1967); see Sakamoto and Yoshida (1996).