Conditional robustness in location estimation

Abstract

SUMMARY Let Y 1 ,…, Y n denote independent real-valued observations, each distributed according to a density p (y − θ ), where θ is an unknown parameter and p is a symmetric density function. This paper considers robust point estimation of θ from the point of view of conditional inference. Specific measures of the conditional robustness of a location estimator are introduced, as well as measures of the conditional robustness of a particular sample. Location-scale models are also considered. The results are applied to several data sets.