New Results on the Small-Sample Properties of Some Robust Univariate Estimators of Location

This article compares eight estimators in terms of relative efficiencies with the univariate mean, some of which have not been compared previously. Four estimators, when testing hypotheses, are compared in terms of actual Type I errors. In terms of point estimation, the modified one-step M-estimator, one-step M-estimator, and rfch estimator are found to be the three best choices depending on the proportion of outliers. In terms of actual Type I errors, the modified one-step M estimator's and rfch estimator's level was between .045 and .055 in 5 out of 7 situations when real data were used in simulations.