Geodesic
On geometry of the set of admissible quadratic estimators of quadratic functions of normal parameters
Discussiones Mathematicae. Probability and Statistics, Tome 26 (2006) no. 2, pp. 109-125.

Voir la notice de l'article provenant de la source Library of Science

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.
Keywords: linear estimator, quadratic estimator, Bayesian quadratic estimator, quadratic loss function, admissibility, quadratic subspace 
@article{DMPS_2006_26_2_a0,
     author = {Neumann, Konrad and Zontek, Stefan},
     title = {On geometry of the set of admissible quadratic estimators of quadratic functions of normal parameters},
     journal = {Discussiones Mathematicae. Probability and Statistics},
     pages = {109--125},
     publisher = {mathdoc},
     volume = {26},
     number = {2},
     year = {2006},
     zbl = {1128.62005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMPS_2006_26_2_a0/}
}
TY  - JOUR
AU  - Neumann, Konrad
AU  - Zontek, Stefan
TI  - On geometry of the set of admissible quadratic estimators of quadratic functions of normal parameters
JO  - Discussiones Mathematicae. Probability and Statistics
PY  - 2006
SP  - 109
EP  - 125
VL  - 26
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMPS_2006_26_2_a0/
LA  - en
ID  - DMPS_2006_26_2_a0
ER  - 
%0 Journal Article
%A Neumann, Konrad
%A Zontek, Stefan
%T On geometry of the set of admissible quadratic estimators of quadratic functions of normal parameters
%J Discussiones Mathematicae. Probability and Statistics
%D 2006
%P 109-125
%V 26
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMPS_2006_26_2_a0/
%G en
%F DMPS_2006_26_2_a0
Neumann, Konrad; Zontek, Stefan. On geometry of the set of admissible quadratic estimators of quadratic functions of normal parameters. Discussiones Mathematicae. Probability and Statistics, Tome 26 (2006) no. 2, pp. 109-125. http://geodesic.mathdoc.fr/item/DMPS_2006_26_2_a0/

[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.