ABSTRACT
We noted previously (Chapter 2) that, under the assumptions of the strong classical linear regression model, the OLS estimates of the regression intercept (β0) and slope (β1) have certain desirable or optimal properties. For this model, a key assumption concerning the random error term ε was that it followed a normal distribution with zero mean and constant variance. (Under normality, the OLS estimates are also maximum-likelihood estimates.) We also noted (Chapter 4) that, if we were unsure of the form of ε’s probability density function, then a nonparametric (e.g., rank-based) regression method was called for. However, it may be the case that the probability density function of ε departs only slightly from the aforementioned normal form. In this situation, a regression method intermediate to OLS and nonparametric regression is warranted. Such a method is referred to as robust regression.
