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Comparison of linear restricted models with respect to the validity of admissible and linearly sufficient estimators

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  • Markiewicz, Augustyn

Abstract

Two restricted linear models M0 and M are considered. The models can differ in model matrices, dispersion matrices, and possibly in parameter restrictions. The validity under M of estimators that are admissible and linearly sufficient under M0 is studied. Criteria are derived for strong and week validity, i.e. when all estimators and at least one, respectively, preserve their properties. Some supplementary results for unrestricted model are also given.

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  • Markiewicz, Augustyn, 1998. "Comparison of linear restricted models with respect to the validity of admissible and linearly sufficient estimators," Statistics & Probability Letters, Elsevier, vol. 38(4), pages 347-354, July.
    • Handle: RePEc:eee:stapro:v:38:y:1998:i:4:p:347-354
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    References listed on IDEAS

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    1. Baksalary, Jerzy K. & Mathew, Thomas, 1988. "Admissible linear estimation in a general Gauss-Markov model with an incorrectly specified dispersion matrix," Journal of Multivariate Analysis, Elsevier, vol. 27(1), pages 53-67, October.
    2. Mueller, Jochen, 1987. "Sufficiency and completeness in the linear model," Journal of Multivariate Analysis, Elsevier, vol. 21(2), pages 312-323, April.
    3. Rao, C. Radhakrishna, 1973. "Representations of best linear unbiased estimators in the Gauss-Markoff model with a singular dispersion matrix," Journal of Multivariate Analysis, Elsevier, vol. 3(3), pages 276-292, September.
    4. Markiewicz, Augustyn, 1996. "Characterization of general ridge estimators," Statistics & Probability Letters, Elsevier, vol. 27(2), pages 145-148, April.
    5. Heiligers, Berthold & Markiewicz, Augustyn, 1996. "Linear sufficiency and admissibility in restricted linear models," Statistics & Probability Letters, Elsevier, vol. 30(2), pages 105-111, October.
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    Cited by:

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    3. Liu, Xu-Qing & Rong, Jian-Ying & Liu, Xiu-Ying, 2008. "Best linear unbiased prediction for linear combinations in general mixed linear models," Journal of Multivariate Analysis, Elsevier, vol. 99(8), pages 1503-1517, September.
    4. Liu, Xu-Qing & Wang, Dong-Dong & Rong, Jian-Ying, 2009. "Quadratic prediction and quadratic sufficiency in finite populations," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 1979-1988, October.

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