The effect of an outlier on L-estimators of location in symmetric distributions

Abstract

The effect is studied of an outlier which has the same symmetric distribution as the other observations except for a change in location and a possible increase in scale. We show that the median is the most bias-resistant estimator, in the class of L -statistics with symmetric nonnegative coefficients that add up to one, for a class of distributions which includes the normal, double-exponential and logistic distributions.