A Two-Stage Procedure for Fixed-Size Confidence Region When Covariance Matrices Have Some Structures

The problem of constructing a fixed-size confidence region for a linear function of mean vectors of k multinormal populations is considered when auxiliary information about covariance matrices exists. A two-stage procedure is proposed to derive such a confidence region by incorporating such information. The proposed two-stage procedure is asymptotically efficient and more economical than a previous attempt given by Aoshima, Takada and Srivastava (1997) in terms of the sample size.