All Admissible Linear Estimators of a Multivariate Poisson Mean
Admissible linear estimators Mx + γ must be pointwise limits of Bayes estimators. Using properties of Bayes estimators preserved by taking limits, the structure of M and γ can be determined. Among M, γ with this structure, a necessary and sufficient condition for admissibility is obtained. This cond...
| Veröffentlicht in: | The Annals of Statistics. - Institute of Mathematical Statistics. - 13(1985), 1, Seite 282-294 |
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| Format: | Online-Aufsatz |
| Sprache: | English |
| Veröffentlicht: |
1985
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| Zugriff auf das übergeordnete Werk: | The Annals of Statistics |
| Schlagworte: | Estimation multivariate Poisson parameter decision theory linear estimators admissibility linear models Mathematics Behavioral sciences Information science Philosophy |
| Zusammenfassung: | Admissible linear estimators Mx + γ must be pointwise limits of Bayes estimators. Using properties of Bayes estimators preserved by taking limits, the structure of M and γ can be determined. Among M, γ with this structure, a necessary and sufficient condition for admissibility is obtained. This condition is applied to the case of linear (mixture) models. It is shown that only the most trivial such models admit linear estimators of full rank which are admissible or are even limits of Bayes estimators. |
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| ISSN: | 00905364 |