A universal robustification procedure

TL;DR

This paper introduces a universal method to modify estimators, making their asymptotic distribution robust against data contamination, supported by new theoretical insights into quantiles.

Contribution

It presents a novel universal robustification procedure applicable to a wide class of estimators, with theoretical validation in finite and infinite dimensions.

Findings

Transforms estimators into robust asymptotically normal estimators

Proves new properties of componentwise and geometric quantiles

Applicable in finite and infinite-dimensional settings

Abstract

We develop a procedure that transforms any asymptotically normal estimator into an asymptotically normal estimator whose distribution is robust to arbitrary data contamination. More generally, our procedure transforms any estimator whose asymptotic distribution has positive and continuous density at the origin into an asymptotically normal estimator whose distribution is robust to arbitrary contamination. In developing such a procedure we prove new general properties of componentwise and geometric quantiles in both finite and infinite dimensions.