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.
"On Preliminary Test and Shrinkage $M$-Estimation in Linear Models." Ann. Statist. 15 (4) 1580 - 1592, December, 1987. https://doi.org/10.1214/aos/1176350611