The breakdown and influence properties of outlier rejection-plus-mean procedures

In a recent paper, Hampel (1985) studied the properties of rejection-plus-mean procedures as estimators of a location parameter. He reported that these procedures have low breakdown and high variance. In this article it is pointed out that these results are due to the outliers being rejected in a forwards-stepping manner, and when a more appropriate backwards-stepping approach is used, rejection-plus-mean procedures lead to estimators with high breakdown and high variance. In this article it is pointed out that these results are due to the outliers being rejected in a forwards-stepping manner, and when a more appropriate backwards-stepping approach is used, rejection-plus-mean procedures lead to estimator with high breakdown and redescending theoretical influence function.