Some properties of the best linear unbiased estimators in multivariate growth curve models

Abstract

The purpose of this article is to build a class of the best linear unbiased estimators (BLUE) of the linear parametric functions, to prove some necessary and sufficient conditions for their existence and to derive them from the corresponding normal equations, when a family of multivariate growth curve models is considered. It is shown that the classical BLUE known for this family of models is the element of a particular class of BLUE built in the proposed manner. The results are expressed in a convenient computational form by using the coordinate-free approach and the usual parametric representations.