High Robustness and High Efficiency of Estimation

Abstract

In this chapter we regard weakly asymptotically linear estimators which are robust for shrinking contamination (see Definition 5.4). In Section 7.1 we characterize “most robust” estimators in linear models, which are weakly asymptotically linear estimators with minimum asymptotic bias for shrinking contamination. We also characterize designs which minimize the asymptotic bias of robust estimation. In Section 7.2 we characterize weakly asymptotically linear estimators in linear models which minimize the trace of the asymptotic covariance matrix within all estimators with an asymptotic bias for shrinking contamination, which is bounded by some bias bound b. Also optimal designs for optimal robust estimation are derived. In Section 7.3 we present efficient robust estimators and designs for estimating a nonlinear aspect in a linear model and in Section 7.4 for estimation in a nonlinear model.