Some Comments on the Watson Efficiency of the Ordinary Least Squares Estimator Under the Gauss Markov Model

Abstract

We consider the estimation of a given estimable parametric function in the Gauss–Markov model, and focus on questions concerning the Watson efficiency of the ordinary least squares estimator (OLSE) of the given parametric function with respect to the best linear unbiased estimator (BLUE). We apply the Frisch–Waugh–Lovell Theorem for the estimation of the parametric function, and give an interesting decomposition of the total Watson efficiency with respect to the efficiency of the parametric function. Also, a relation between the Watson efficiency of the OLSE of the given parametric function and specific canonical correlations is established.