Estimation and hypothesis testing in mixed linear models

Dissertação apresentada para obtenção do Grau de Doutor em Matemática, Estatística, pela Universidade Nova de Lisboa, faculdade de Ciências e Tecnologia

This thesis focuses on inference and hypothesis testing for parameters in orthogonal mixed linear models. A canonical form for such models is obtained using the matrices in principal basis of the commutative Jordan algebra associated to the model. UMVUE are derived and used for hypothesis tests. When usual F tests are not possible to use, generalized F tests arise, and the distribution for the statistic of such tests is obtained under some mild conditions. application of these results is made to cross-nested models.