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2006 | 26 | 2 | 109-125
Tytuł artykułu

On geometry of the set of admissible quadratic estimators of quadratic functions of normal parameters

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We consider the problem of admissible quadratic estimation of a linear function of μ² and σ² in n dimensional normal model N(Kμ,σ²Iₙ) under quadratic risk function. After reducing this problem to admissible estimation of a linear function of two quadratic forms, the set of admissible estimators are characterized by giving formulae on the boundary of the set D ⊂ R² of components of the two quadratic forms constituting the set of admissible estimators. Different shapes and topological properties of the set D are studied.
Rocznik
Tom
26
Numer
2
Strony
109-125
Opis fizyczny
Daty
wydano
2006
otrzymano
2005-11-10
poprawiono
2006-10-20
Twórcy
  • Faculty of Mathematics, Computer Science and Econometrics University of Zielona Góra prof. Z. Szafrana 4a, 65-516 Zielona Góra, Poland
  • Faculty of Mathematics, Computer Science and Econometrics University of Zielona Góra prof. Z. Szafrana 4a, 65-516 Zielona Góra, Poland
Bibliografia
  • [1] S. Gnot, E. Rafajłowicz and A. Urbańska-Motyka, Statistical inference in a linear model for spatially located sensors and random input, Ann. Inst. Statist. Math. 53. 2 (2001), 370-379.
  • [2] S. Gnot and J. Kleffe, Quadratic estimation in mixed linear models with two variance components, J. Statist. Plann. Inference 8 (1983), 267-279.
  • [3] D.A. Harville, Quadratic unbiased estimation of two variance components for the one-way classification, Biometrika 56 (1969), 313-326.
  • [4] L.R. LaMotte, Admissibility in linear model, Ann. Statist. 19 (1982), 245-256.
  • [5] L.R. LaMotte, Admissibility, unbiasedness, and nonnegativity in the balanced, random, one-way anova model, Linear statistical inference (Poznań, 1984), Lecture Notes in Statist. 35 (1985), 184-199.
  • [6] K. Neumann and S. Zontek, On geometry of the set of admissible invariant quadratic estimators in balanced two variance components model, Statistical Papers 45 (2004), 67-80.
  • [7] A.L. Rukhin, Quadratic estimators of quadratic functions of normal parameters, J. Statist. Plann. Inference 15 (1987), 301-310.
  • [8] A.L. Rukhin, Admissible polynomial estimates for quadratic polynomials of normal parameters (in russian), Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. 184, Issued. Mat. Statist. 9 (1990), 234-247.
  • [9] R. Zmyślony, Quadratic admissible estimators, (in polish) Roczniki Polskiego Towarzystwa Matematycznego, Seria III: Matematyka Stosowana VII, (1976), 117-122.
  • [10] S. Zontek, Admissibility of limits of the unique locally best linear estimators with application to variance components models, Probab. Math. Statist. 9. 2 (1988), 29-44.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1077
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