The Metrically Trimmed Mean as a Robust Estimator of Location

Abstract

The metrically trimmed mean is defined as the average of observations remaining after a fixed number of outlying observations have been removed. A metric, the distance from the median, is used to determine which points are outlying. The influence curve and the asymptotic normality of the metrically trimmed mean are derived using von Mises expansions. The relative merits of the median, the trimmed mean and the metrically trimmed mean are discussed in neighborhoods of nonparametric models with natural parameters. It is observed that the metrically trimmed mean works well for the center of symmetry of a symmetric distribution function with asymmetric contamination. A multivariate extension of the metrically trimmed mean is discussed.