Chapter 3: Estimation in the Linear Model

Abstract:

Consider the homoscedastic linear model

which we represent by (y, X β, σ² I). This is a special case of the model described in (1.4)–(1.5), with the restrictions that the model errors (elements of the vector ε) have a common variance and are uncorrelated. We assume that y is a vector of n elements, X is an n × p matrix with n > p and β is a vector of p elements. The unknown parameters of this model are the coefficient vector β and the error variance σ². In this chapter we deal with the problem of estimation of these parameters from the observables y and X…