Pre-Test type estimators for selection of simple normal models

Abstract

Suppose that the observed k-vector T is N(0, a21)-distributed and that some of the components of 0 may be zero. We wish to simultaneously select and estimate the non-zero components of 0 . Let 0(T, q ) be the estimatorwhose i-th component is either 0 if T, is qne of the q components of T closest to 0 or T otherwise. We study three ways to estimate the risk of 0 ( T , q). Minimizing each risk estimator in q leads to three ways to choose q in B(T, q). The resulting estimators are compared with respect to their risks in terms of squared error with complexity cost loss. It turns out that they perform rather similarly and that they largely improve on previous estimators in this setting.