Summary: The influence functions of the regression trimmed-mean estimators proposed by R. Koenker and G. Bassett [Econometrica 46, 33-50 (1978; Zbl 0373.62038)] and A. H. Welsh [Ann. Stat. 15, 20-36 (1987; Zbl 0618.62074)] are bounded in the dependent-variable space but not in the independent-variable space. This article follows an unpublished approach of C. L. Mallows and modifies these estimators so that the resulting estimators have bounded-influence functions.
The large-sample behavior of these estimators is studied, and it is shown that they have the same asymptotic distribution. The small-sample behaviors of the ordinary-regression and bounded-influence-regression trimmed means are then investigated by means of a Monte Carlo study and by applying the estimators to water-salinity data. Based on these results we conclude that one can potentially gain much by using bounded- influence-regression trimmed means over ordinary-regression trimmed means; however, there does not seem to be a clear choice between the Koenker-Bassett and Welsh versions.