Commutative orthogonal block structure: Orthogonal features

Abstract

An interesting class of models with orthogonal block structure, OBS, are the ones with commutative orthogonal block structure, COBS. In such class of models the least square estimators are best linear unbiased estimators. In our approach we will consider the orthogonal partition Y = YΩ+YΩ⊥ where YΩ and YΩ⊥ are the orthogonal projections of the observations vector on the space Ω spanned by the mean vector and its orthogonal complement. When normality is assumed, we will obtain UMVUE estimators for the variance components in the family of estimators that depend only on YΩ⊥. When μ = X0β0 and the components of β0 correspond to the treatments of a fixed effects design Π, we show how to test for absence of effects and interaction for the factors in Π.