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

Discussiones Mathematicae Probability and Statistics (2006)

- Volume: 26, Issue: 2, page 109-125
- ISSN: 1509-9423

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topKonrad Neumann, and Stefan Zontek. "On geometry of the set of admissible quadratic estimators of quadratic functions of normal parameters." Discussiones Mathematicae Probability and Statistics 26.2 (2006): 109-125. <http://eudml.org/doc/277042>.

@article{KonradNeumann2006,

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.},

author = {Konrad Neumann, Stefan Zontek},

journal = {Discussiones Mathematicae Probability and Statistics},

keywords = {linear estimator; quadratic estimator; Bayesian quadratic estimator; quadratic loss function; admissibility; quadratic subspace},

language = {eng},

number = {2},

pages = {109-125},

title = {On geometry of the set of admissible quadratic estimators of quadratic functions of normal parameters},

url = {http://eudml.org/doc/277042},

volume = {26},

year = {2006},

}

TY - JOUR

AU - Konrad Neumann

AU - Stefan Zontek

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

JO - Discussiones Mathematicae Probability and Statistics

PY - 2006

VL - 26

IS - 2

SP - 109

EP - 125

AB - 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.

LA - eng

KW - linear estimator; quadratic estimator; Bayesian quadratic estimator; quadratic loss function; admissibility; quadratic subspace

UR - http://eudml.org/doc/277042

ER -

## References

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