All Admissible Linear Estimators of a Multivariate Poisson Mean
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Penn collection
Statistics Papers
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estimation
multivariate Poisson parameter
decision theory
linear estimators
admissibility
linear models
Statistics and Probability
multivariate Poisson parameter
decision theory
linear estimators
admissibility
linear models
Statistics and Probability
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Brown, Lawrence D
Farrell, R. H
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Abstract
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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1985
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Annals of Statistics