De Jongh, P. J.De Wet, T.Welsh, A. H.2025-06-172025-06-170162-1459http://www.scopus.com/inward/record.url?scp=84950422090&partnerID=8YFLogxKhttps://hdl.handle.net/1885/733764102The influence functions of the regression trimmed-mean estimators proposed by Koenker and Bassett (1978) and Welsh (1987) are bounded in the dependent-variable space but not in the independent-variable space. This article follows the approach of Mallows (1973, 1975) 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 (see Ruppert and Carroll 1980). 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.6enInfluence functionInfluential observationRobust regression198810.1080/01621459.1988.1047866784950422090