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On decomposing the Watson efficiency of ordinary least squares in a partitioned weakly singular linear model. (English) Zbl 1193.62094
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.

MSC:
62H12 Estimation in multivariate analysis
62J05 Linear regression; mixed models
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