Robust Statistics

Introduction

The term “robust” was introduced into the statistical literature by Box (1953). By then, robust methods such as trimmed means, had been in sporadic use for well over a century, see for example Anonymous (1821). However, Tukey (1960) was the first person to recognize the extreme sensitivity of some conventional statistical procedures to seemingly minor deviations from the assumptions, and to give an eye-opening example. His example, and his realization that statistical methods optimized for the conventional Gaussian model are unstable under small perturbations were crucial for the subsequent theoretical developments initiated by Huber (1964) and Hampel (1968).

In the 1960s robust methods still were considered “dirty” by most. Therefore, to promote their reception in the statistical community it was crucial to mathematize the approach: one had to prove optimality properties, as was done by Huber’s minimax results (1964, 1965, 1968), and to give a formal definition of...