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On geometry of the set of admissible invariant quadratic estimators in balanced two variance components model

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Abstract

Two variance components model for which each invariant quadratic admissible estimator of a linear function of variance components (under quadratic loss function) is a linear combination of two quadratic forms,Z 1,Z 2, say, is considered. A setD={(d 1,d 2)′:d 1 Z 1+d 2 Z 2 is admissible} is described by giving formulae on the boundary ofD. Different forms of the setD are presented on figures.

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References

  1. S. Gnot and J. Kleffe (1983). Quadratic estimation in mixed linear models with two variance components.J. Statist. Plann. Inference,8, 267–279.

    Article  MATH  MathSciNet  Google Scholar 

  2. S. Gnot, E. Rafajłowicz and A. Urbańska-Motyka (2001). Statistical inference in a linear model for spatially located sensors and random input.Ann. Inst. Statist. Math.,53.2, 370–379.

    Article  MATH  MathSciNet  Google Scholar 

  3. L. R. LaMotte (1982). Admissibility in linear models.Ann. Statist.,10, 245–256.

    Article  MATH  MathSciNet  Google Scholar 

  4. A. Olsen, J. Seely and D. Birkes (1976). Invariant quadratic unbiased estimation for two variance components.Ann. Statist.,4, 876–890

    Article  MathSciNet  Google Scholar 

  5. J. Seely (1971). Quadratic subspaces and completeness.Ann. Math. Statist.,42, 710–721.

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Institute of Mathematics, University of Zielona Góra, ul. prof. Z. Szafrana 4a, 65-516, Zielona Góra, Poland

    Konrad Neumann & Stefan Zontek

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  1. Konrad Neumann
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  2. Stefan Zontek
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Neumann, K., Zontek, S. On geometry of the set of admissible invariant quadratic estimators in balanced two variance components model. Statistical Papers 45, 67–80 (2004). https://doi.org/10.1007/BF02778270

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  • DOI: https://doi.org/10.1007/BF02778270

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