Point Estimation and Tests of Hypotheses in Small Samples

Abstract

The ordinary least squares and generalized least squares results reviewed in Chapter 2 dealt with the efficiency of estimation methods in the classical linear regression model and the generalized least squares model. However, small sample statistical inference based on these estimators requires stronger distributional assumptions on the error terms than those made in the previous chapter. In this chapter the distributional properties of the error terms in the classical linear regression model are assumed but, in addition, the error terms are assumed to be normally distributed. This “revised” model is called the classical normal linear regression model. It permits maximum likelihood estimation of the parameters and the construction of likelihood ratio tests of hypotheses.