ArticleOriginal scientific text

Title

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

Authors 1, 1

Affiliations

  1. Faculty of Mathematics, Computer Science and Econometrics University of Zielona Góra prof. Z. Szafrana 4a, 65-516 Zielona Góra, Poland

Abstract

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

Bibliography

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Pages:
109-125
Main language of publication
English
Received
2005-11-10
Accepted
2006-10-20
Published
2006
Exact and natural sciences