A Fundamental Partition in Models with Commutative Orthogonal Block Structure

Abstract

Models with commutative orthogonal block structure, COBS, constitute an interesting class of models with orthogonal block structure, OBS, in which the orthogonal projection matrix on the space Ω spanned by the mean vectors commute with the known pairwise orthogonal projection matrices Q1,…, Qm that figure in the expression of the variance‐covariance matrix V = ∑ j = 1mγjQj of the model. We discuss the importance of the orthogonal partition Y = YΩ+YΩ⊥ where Y, YΩ and YΩ⊥ are the observation vectors and its orthogonal projection on Ω. and Ω⊥, the orthogonal complement on parameters estimation.