Introduction

Abstract

In the classical methodology of least-squares regression the conditional mean function, the function that describes how the mean of y changes with the vector of covariates x, is (almost) all we need to know about the relationship between y and x. This is often perceived as the ‘systematic component’ around which y fluctuates due to an “erratic component”. The crucial, and convenient, thing about this view is that the error is assumed to have precisely the same distribution whatever values may be taken by the components of the vector x. If this is the case, we can be fully satisfied with an estimated model of the conditional mean function, supplemented perhaps by an estimate of the conditional dispersion of y around its mean.