On the existence of the Gauss-Markov estimators in linear mixed models

Abstract

The purpose of this article is to present a simpler way to verify the existence of the Gauss-Markov estimators (GME) of the expected mean which are both the best linear unbiased estimators (BLUE) of the mean in a multivariate mixed linear model and the best quadratic unbiased estimators (BQUE) of the covariance components in a new linear model built from the initial one. The results are expressed in a coordinate-free approach in order to accord them an intuitive representation in finite dimensional Hilbert spaces.