Sufficient and admissible estimators in general multivariate linear model

The notion of linear sufficiency in general Gauss–Markov model is extended to a general multivariate linear model for any specific set of estimable functions. A general formula of the difference between the dispersion matrix of the BLUE in the original model and that in the transformed model is prov...

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Bibliographic Details
Published in:Journal of statistical planning and inference 2005-12, Vol.135 (2), p.371-383
Main Authors: Ip, Wai-cheung, Heung Wong, Liu, Jin-shan
Format: Article
Language:English
Subjects:
Admissibility
BLUE
Exact sciences and technology
General multivariate linear model
General topics
Linear inference, regression
Linear sufficiency
Mathematical analysis
Mathematics
Measure and integration
Probability and statistics
Sciences and techniques of general use
Statistics
Sufficiency and information
Transformed observations
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Summary:The notion of linear sufficiency in general Gauss–Markov model is extended to a general multivariate linear model for any specific set of estimable functions. A general formula of the difference between the dispersion matrix of the BLUE in the original model and that in the transformed model is provided, which brings some further contributions to the theory of linear sufficiency. Moreover, a general formula of the change of BLUE due to transformation is obtained. The analysis here leads to some results, some of which are known in the literature. Besides linear sufficiency, the admissibility of a linear statistic is also extended to the multivariate case.
ISSN:0378-3758
1873-1171
DOI:10.1016/j.jspi.2004.05.005