On Weighted Randomly Trimmed Means

A class of robust location estimators called weighted randomly trimmed means are introduced and not only their consistency and asymptotic normality are proved, but their influence functions, asymptotic variances and breakdown points are also derived. They possess the same breakdown points as the median, and some of them own higher asymptotic relative efficiencies at the heavy-tailed distributions than some other well-known location estimators; whereas the trimmed means, Winsorized means and Huber’s M-estimator possess higher asymptotic relative efficiencies at the light-tailed distributions, in which Huber’s M-estimator is the most robust.