Robustness

Abstract

Many inference methods were presented in previous chapters for multivariate normal populations. A question of theoretical and utmost practical importance is the effect of non-normality on the inference. For example, what happens if the likelihood ratio test of sphericity, derived assuming normality, is performed, but, in fact, the population follows a multivariate student distribution on 10 degrees of freedom? Is the significance level of α = 5%, say, still close to 5%? The theory of robustness gives answers as to how sensitive multivariate normal inferences are to departures from normality. Most importantly, it proposes some remedies, i.e., more procedures. In Section 13.2, we present some non-normal models often used in robustness, the so-called elliptical distributions. The rest of the chapter is devoted to robust estimation and adjusted likelihood ratio tests.