**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

By

K.L. Chu, 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.