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Some further results concerning the decomposition of the Watson efficiency in partitioned linear models. (English) Zbl 1193.62095
Summary: While considering the estimation of regression coefficients in a partitioned weakly singular linear model, the authors [ibid., 634–351 (2004; Zbl 1193.62094)] introduced a particular decomposition for the Watson efficiency of the ordinary least squares estimator. This decomposition presents the “total” Watson efficiency as a product of three factors. In this paper we give new insight into the decomposition showing that all three factors are related to the efficiencies of particular submodels or their transformed versions. Moreover, we prove an interesting connection between a particular reduction of the Watson efficiency and the concept of linear sufficiency. We shortly review the relation between efficiency and specific canonical correlations. We also introduce the corresponding decomposition for the Bloomfield–Watson commutator criterion, and give a necessary and sufficient condition for its specific reduction.

MSC:
62H12 Estimation in multivariate analysis
62J05 Linear regression; mixed models
62B05 Sufficient statistics and fields
62H20 Measures of association (correlation, canonical correlation, etc.)
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