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Admissible linear estimation in a general Gauss-Markov model with an incorrectly specified dispersion matrix. (English) Zbl 0665.62011
Necessary and sufficient conditions are established for the set of all admissible linear estimators under \({\mathbb{M}}_ 0\) to be contained in the corresponding set of estimators under \({\mathbb{M}}\), where \({\mathbb{M}}_ 0\) and \({\mathbb{M}}\) are general Gauss-Markov models with identical model matrices but different dispersion matrices. As preliminary results, certain new characterizations of admissible linear estimators are derived, including explicit expressions for the general representations of such estimators and extensions of the admissibility criteria given by C. R. Rao [Ann. Statist. 4, 1023-1037 (1976; Zbl 0336.62055)] and W. Klonecki and S. Zontek [J. Multivariate Anal. 24, 11-30 (1988)].

MSC:
62C15 Admissibility in statistical decision theory
62J05 Linear regression; mixed models
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