Generalized Least Square Estimation

Abstract

In this chapter the fundamental concepts of the growth curve model (GCM) are introduced and several commonly encountered forms of the GCM are described through a variety of practical examples in biology, agriculture, and medical research. Some basic statistical inference of the GCM, such as generalized least square estimate (GLSEs) and the admissibility of estimates on linear combinations of regression coefficients, are discussed in detail. It is shown that the GLSE of the regression coefficient is also the best linear unbiased estimate (BLUE) in the sense of the matrix loss function. In addition, the necessary and sufficient conditions of admissible estimates on linear combinations of regression coefficients are studied. The main theme of this chapter is to demonstrate the use of the GCM in practice and to comprehensively introduce the theory of generalized least square estimation as well. Maximum likelihood estimate (MLE) and restricted maximum likelihood (REML) estimate will be discussed in Chapter 3.