Estimation and incommutativity in mixed models

Abstract

In this paper we present a treatment for the estimation of variance components and estimable vectors in linear mixed models in which the relation matrices may not commute. To overcome this difficulty, we partition the mixed model in sub-models using orthogonal matrices. In addition, we obtain confidence regions and derive tests of hypothesis for the variance components. A numerical example is included. There we illustrate the estimation of the variance components using our treatment and compare the obtained estimates with the ones obtained by the ANOVA method. Besides this, we also present the restricted and unrestricted maximum likelihood estimates.

Estimation in additive models and ANOVA-like applications

“…, Z m , respectively). These models are easy to implement, not requiring structural conditions to be fulfilled, see [10]. Such conditions, such as blocks with the same size, and orthogonal block structure, have played an important part in the study of models (see for instance [4,5]).…”