**Contributed talks on Block Orthogonalization**

The aim of this paper is to obtain estimators for estimable vectors that are UMVUE [UBLUE] when normality is assumed [in general] under conditions that do not involve the orthogonal projection matrix $T$ on the space $\Omega$ spanned by the mean vector. Namely we consider models whose variance-covariance matrices are all the positive definite linear combinations $V(\gamma)= \sum_{j=1}^{m} \gamma_{j} K_{j},$ where the $K_{1},...,K_{m}$ are pairwise orthogonal orthogonal projection matrices, POOPM, that add up to $I_{n}.$ So that $\gamma \in \mathbb{R}^{m}_{>},$ with $\mathbb{R}^{m}_{>}$ $[\mathbb{R}^{m}_{\geq}]$ the family of vectors with positive [non negative] components of subspace $\mathbb{R}^{m}.$ If we only required $V(\gamma)$ to be semi-positive definite we would have $\gamma \in \mathbb{R}^{m}_{\geq},$ and the model, would have orthogonal block structure, OBS. We may say that the models we are considering have positive OBS, POBS.

Application to a real data set is also presented.

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