The Effect of Sample Heterogeneity on Linear Functions of Order Statistics, with Applications to Robust Estimation

Abstract

Abstract In a certain sense sample heterogeneity can only decrease the variance of a linear function of order statistics compared with that for a homogeneous sample, and thus the variance of those statistics will tend to be overestimated. The magnitude of this effect for robust estimators of location and scale is described, with particular reference to contamination models. It is shown that with asymmetric contamination, extreme observations may have much less influence on these estimators than is generally believed, if trimming is employed.