Robust Estimation in Dependent Situations

Abstract

To analyze the effect of correlation in random samples on the performance of estimators of location, small correlation approximations for the asymptotic variance are found. Approximately optimal estimators (in the asymptotic minimax sense of Huber) are presented and compared to other estimators in terms of maximum asymptotic variance over the class of $\varepsilon$-contaminated normals. The presence of relatively small correlation can drastically inflate variances, and the optimal rules given here offer substantial improvements over previously considered estimators.