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ABSTRACT
We consider a general partitioned linear model and its stochastically restricted model without any rank assumptions. We give necessary and sufficient conditions for the equalities of the ordinary least-squares estimators (OLSEs) and the best linear unbiased estimators (BLUEs) of
and the equalities of the OLSEs and BLUEs of
under a general partitioned linear model and its stochastically restricted model. Also, we give an example for the equality of the BLUEs of
under a general linear model and its stochastically restricted model.