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

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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 
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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/