Abstract
For a univariate linear model Yn=Xnθ+εn, when it is apriori suspected that Hθ=h may hold, we are interested in robust estimates of θ. Four classes of point estimations, namely, the unrestricted R-estimators (URE), restricted R-estimators (RRE), the preliminary test R-estimators (PTRE) and shrinkage R-estimators (SRE) are considered. In the light of asymptotic distributional risks, their relative efficiency results under local alternatives are studied in details. Although the SRE may dominate the URE, neither of the SRE nor PTRE dominate each other. We may conclude that the SRE and PTRE are robust relative to the URE and RRE. Furtheremore four versions of M-estimatiors corresponding to the URE, RRE, PTRE and SRE are proposed and the results similar to the cases of the R-estimators are discussed briefly.
