On Local Asymptotic Minimaxity and Admissibility in Robust Estimation

Abstract

For a particular pseudoloss function, local asymptotic minimaxity and admissibility in the sense of Hajek and Le Cam are studied when probability measures are replaced by certain capacities ($\epsilon$-contamination, total variation). A minimax bound for arbitrary estimator sequences is established, admissibility of minimax estimators is proved, and it is shown that minimax estimators must necessarily have an asymptotic expansion in terms of a truncated logarithmic derivative.