Robustification and performance evaluation of empirical risk measures and other vector-valued estimators

摘要

Actuarial axioms lead to risk measures that for loss distributions assign weighted integrals of the corresponding value-at-risk functions. Hence, constructing robust and efficient estimators for the integrals using observed losses becomes a task of practical interest. Furthermore, a number of risk measures are functionals of several such weighted integrals. Hence, in order to cover many cases of practical interest, in the present paper we consider robust estimators of vector-valued risk measures as well as other population parameters, and we also study their large-sample efficiency properties. In addition, we discuss robust estimators for location, scale, and location-scale parameters for several parametric families of interest in actuarial science, econometrics, and beyond.