Operations with Iso-structured models with commutative orthogonal block structure: An introductory approach

Abstract

An approach to models based on an algebraic context allows interesting and useful statistical results to be derived or at least better understood. In the approach to models with commutative orthogonal block structure via algebraic structure it is possible to show that the orthogonal projection matrix in the space spanned by the mean vector commuting with the covariance matrix guarantees least squares estimators giving best linear unbiased estimators for estimable vectors. In this work we focus on the possibility of performing operations with models with commutative orthogonal block structure that are iso-structured, that is, models generating the same commutative Jordan Algebra of symmetric matrices.