FIXED-SIZE CONFIDENCE REGION BY MULTIVARIATE TWO-STAGE PROCEDURE WHEN THE COVARIANCE MATRIX HAS A STRUCTURE

Abstract

The problem of constructing fixed-size confidence regions for estimating the multinormal mean is considered when auxiliary information about the covariance matrix exists. Incorporating such information, we propose a two-stage procedure which meets the requirement and is asymptotically efficient. Furthermore, it turns out that the procedure requires less observations than the usual one.