Adaptive choice of trimming proportion in trimmed least-squares estimation

We propose partially adaptive estimators of the trimming proportion [alpha] for the trimmed mean in the location modeling and for the trimmed least-squares estimator of Koenker and Bassett (1978) in the linear regression model. The adaptive estimators are based on Hájek's (1970) rank-based decision procedure which selects one of a finite family of distribution shapes and on its extension based on regression rank scores of Gutenbrunner and Jurecková (1992). The procedures are invariant to the location and scale in the location model and to the regression and scale in the regression model, respectively; hence there is no need of estimation of the pertaining parameters.