A (Not So) Quick and Dirty Look at Robust M-Estimation

Abstract

a. Robust estimators, those procedures that distinguish likely from unlikely distributions, sometimes are preferable to either parametric or distribution-free estimations. This WP explores statistical properties of maximum likelihood estimates, or M-Estimates, which are one kind of robust estimators. Analyses and simulations show general suitability and accuracy of one class of robust estimators. The results also show that the worst estimators are the classical parametric estimators and statistical tests. The author concludes that a research loses little by using robust estimators when the data are normally distributed, and risks serious errors using parametric estimators when the data are not normally distributed.