Shrinkage estimation in elliptically contoured distribution with restricted parameter space

Abstract

Abstract This paper deals with the problem of estimating the mean vector of an elliptically contoured distribution with unknown scale matrix, where the mean vector is restricted to an unbounded and closed convex set with a smooth or a piecewise smooth boundary. A shrinkage-type estimator is shown to be better than the maximum likelihood estimator subject to the restriction relative to a quadratic loss.