Mallows-type bounded-influence-regression trimmed means

The 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.