Preliminary test estimation of a vector of parametric functions in the general Gauss-Markov model

Abstract

The theory of preliminary test estimation based on comparing the matrix risks of two competing estimators of β or Xβ under the general Gauss-Markov model { Y, Xβ , σ 2 V }, is extended to the situation where the interest is focused on a given vector of estimable parametric functions. Applicability of this extension is shown in the context of a model in which Xβ=Wγ+Zδ , where γ is the vector of main parameters and δ is the vector of nuisance parameters. As an illustration, preliminary test estimation of a vector of treatment contrasts in a fixed-effect model corresponding to a block design is discussed.