A Procedure for Robust Estimation and Inference in Linear Regression

A procedure which should fit many purposes reasonably well for robust regression estimators and the reluctance to use the straightforward inference based on asymptotics is proposed.

Abstract

Even if robust regression estimators have been around for nearly 20 years, they have not found widespread application. One obstacle is the diversity of estimator types and the necessary choices of tuning constants, combined with a lack of guidance for these decisions. While some participants of the IMA summer program have argued that these choices should always be made in view of the specific problem at hand, we propose a procedure which should fit many purposes reasonably well. A second obstacle is the lack of simple procedures for inference, or the reluctance to use the straightforward inference based on asymptotics. The procedure we propose here is essentially an MM-estimator, augmented by the estimation of its asymptotic covariance matrix to allow for approximate inference. It includes, as an extra feature, a test for a potential bias introduced by the requirement of high efficiency. The implicit and explicit choices which determine the procedure cannot be based on solid results, since finite sample studies are not yet available. The purpose of our proposal is to foster such studies as well as the collection of other experience with it.