A Fundamental Problem

Abstract

In the year 1960, John Tukey published a paper on the so-called contaminated or mixed normal distribution that would have devastating implications for conventional inferential methods based on means. Indeed, any method based on means would, by necessity, suffer from a collection of similar problems. Tukey’s paper had no immediate impact on applied work, however, because it was unclear how to deal with the practical implications of his paper. But it served as the catalyst for the theory of robustness that was subsequently developed by Frank Hampel and Peter Huber, and their results laid the foundation for getting practical solutions to the problems revealed by Tukey.