On decomposing the Watson efficiency of ordinary least squares in a partitioned weakly singular linear model

Abstract

We consider the estimation of regression coefficients in a partitioned weakly singular linear model and focus on questions concerning the Watson efficiency of the ordinary least squares estimator of a subset of the parameters with respect to the best linear unbiased estimator. Certain submodels are also considered. The conditions under which the Watson efficiency in the full model splits into a function of some other Watson efficiencies is given special attention. In particular, a new decomposition of the Watson efficiency into a product of three particular factors appears to be very useful. AMS (2000) subject classification. 62J05, 62H12, 62H20.