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On the structure of admissible linear estimators

Author

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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.

Suggested Citation

  • Klonecki, W. & Zontek, S., 1988. "On the structure of admissible linear estimators," Journal of Multivariate Analysis, Elsevier, vol. 24(1), pages 11-30, January.
    • Handle: RePEc:eee:jmvana:v:24:y:1988:i:1:p:11-30
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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: International Journal for Theoretical and Applied Statistics, Springer, vol. 68(2), pages 157-172, September.
    2. Buatikan Mirezi & Selahattin Kaçıranlar, 2023. "Admissible linear estimators in the general Gauss–Markov model under generalized extended balanced loss function," Statistical Papers, Springer, vol. 64(1), pages 73-92, February.

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