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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1077,
author = {Konrad Neumann and Stefan Zontek},
title = {On geometry of the set of admissible quadratic estimators of quadratic functions of normal parameters},
journal = {Discussiones Mathematicae Probability and Statistics},
volume = {26},
year = {2006},
pages = {109-125},
zbl = {1128.62005},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1077}
}
Konrad Neumann; Stefan Zontek. On geometry of the set of admissible quadratic estimators of quadratic functions of normal parameters. Discussiones Mathematicae Probability and Statistics, Tome 26 (2006) pp. 109-125. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1077/
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