Improved Confidence Estimators for the Usual Multivariate Normal Confidence Set

Abstract

The usual multivariate normal confidence set has reported confidence 1-a, which is equal to its coverage probability. If we take a decision-theoretic view, and attempt to estimate the coverage, we find that 1-a is an inadmissible estimator in more than four dimensions. We establish this fact and, moreover, exhibit a confidence estimator that appears to dominate 1-a. This new confidence statement allows us to attach confidence that is uniformly greater than 1-a. We provide necessary conditions, and strong numerical evidence to support our domination claim.-3-1. Introduction. 1.1 The Model. For the confidence se