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On the structure of admissible linear estimators

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  • Klonecki, W.
  • Zontek, S.

Abstract

Using a technique originated by A. Olsen, J. Seely, and D. Birkes (Ann. Statist. 4 (1976), 878-890) and developed by L. R. LaMotte (Ann. Statist. 10 (1982), 245-256) we establish necessary conditions of C. R. Rao's type (Ann. Statist. 4 (1976), 1023-1037) for a linear estimator to be admissible among the class of linear estimators in a general linear model. They are shown to be sufficient for the regression model with a nonnegative definite covariance matrix and for the model with the mean lying in a subspace and the covariance operators varying through the set of all nonnegative definite symmetric matrices. From these results necessary and/or sufficient conditions for admissibility of nonhomogeneous estimators are also derived.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Multivariate Analysis.

Volume (Year): 24 (1988)
Issue (Month): 1 (January)
Pages: 11-30

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Handle: RePEc:eee:jmvana:v:24:y:1988:i:1:p:11-30

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Keywords: general linear model linear estimators admissibility;

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Cited by:
  1. Ewa Synówka-Bejenka & Stefan Zontek, 2008. "A characterization of admissible linear estimators of fixed and random effects in linear models," Metrika, Springer, vol. 68(2), pages 157-172, September.

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