On the equality of estimators under a general partitioned linear model with parameter restrictions

Abstract

Assume that a linear regression model is written as a partitioned form. In such a case, it is quite convenient to determine the role of each subset of regressors, and to derive estimators of unknown partial parameters in the partitioned model. In this paper, we consider the relationships between the well-known ordinary least-squares estimators (OLSEs) and the best linear unbiased estimators (BLUEs) of the whole and partial mean parameter vectors in a general partitioned linear model with parameter restrictions. We first review some known results on the OLSEs and the BLUEs and their properties under general linear models. We then present a variety of necessary and sufficient conditions for OLSEs to be BLUEs under a general partitioned linear model with parameter restrictions.