BOUNDED RISK POINT ESTIMATION OF A LINEAR FUNCTION OF K MULTINORMAL MEAN VECTORS

Abstract

The problem of constructing an estimator with a risk bounded by a preassigned number is considered for a linear function of mean vectors of k multinormal populations, where all covariance matrices are unknown. A two-stage procedure is proposed to give such an estimator. Some asymptotic properties of the proposed two-stage procedure are discussed. The proposed two-stage procedure improves the Ghosh, Mukhopadhyay and Sen (1997)-type two-stage procedure asymptotically.