Advanced Econometrics Takeshi Amemiya

Robust Regression

2.3.2 Introduction

In Chapter 1 we established that the least squares estimator is best linear unbiased under Model 1 and best unbiased under Model 1 with normality. The theme of the previous section was essentially that a biased estimator may be better than the least squares estimator under the normality assumption. The theme of this section is that, in the absence of normality, a nonlinear estimator may be better than the least squares estimator. We shall first discuss robust estimation in the i. i.d sample case, and in the next subsection we shall generalize the results to the regression case.