期刊名称：Sankhya. Series A, mathematical statistics and probability
印刷版ISSN：0976-836X
电子版ISSN：0976-8378
出版年度：2005
卷号：67
期号：01
出版社：Indian Statistical Institute
摘要：While considering the estimation of regression coefficients in a partitioned weakly singular linear model, Chu, Isotalo, Puntanen and Styan (2004a) 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 the efficiency and specific canonical correlations. We also introduce the corresponding decomposition for the Bloom\-field--Watson commutator criterion, and give a necessary and sufficient condition for its specific eduction.
关键词：Best linear unbiased estimation, Watson efficiency, Gau\ss--Markov model, linear sufficiency, partitioned linear model, reduced linear model.
