On Preliminary Test and Shrinkage M-Estimation in Linear Models

In a general univariate linear model, M-estimation of a subset of parameters is considered when the complementary subset is plausibly redundant. Along with the classical versions, both the preliminary test and shrinkage versions of the usual M-estimators are considered and, in the light of their asymptotic distributional risks, the relative asymptotic risk-efficiency results are studied in detail. Though the shrinkage M-estimators may dominate their classical versions, they do not, in general, dominate the preliminary test versions.