Sankhya: The Indian Journal of Statistics

2004, Volume 66, Pt. 4,  634-651

On Decomposing the Watson Efficiency of Ordinary Least Squares in a Partitioned Weakly Singular  Linear Model


K.L. Chu, McGill University, Montr\'eal, Canada, J. Isotalo, S. Puntanen, University of Tampere, Tampere, Finland    G.P.H. Styan, McGill University, Montr\'eal, Canada

SUMMARY . 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 (1991) subject classification. 62J05, 62H12, 62H20 ;

Key words and phrases. Best linear unbiased estimation, Bloomfield-Watson-Knott inequality, BLUE, BWK inequality, efficiency multiplier, FWL theorem, Frisch-Waugh-Lovell theorem, Gauss-Markov model, OLSE, ordinary least squares, partitioned linear model, reduced linear model, splitting the efficiency, total Watson efficiency, weakly singular linear model, Zyskind-Martin model.

Full paper (PDF)