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...

Ausführliche Beschreibung

Bibliographische Detailangaben
Veröffentlicht in:	The Annals of Statistics. - Institute of Mathematical Statistics. - 13(1985), 1, Seite 282-294
1. Verfasser:	Brown, L. D. (VerfasserIn)
Weitere Verfasser:	Farrell, R. H.
Format:	Online-Aufsatz
Sprache:	English
Veröffentlicht:	1985
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


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100	1		\|a Brown, L. D. \|e verfasserin \|4 aut
245	1	0	\|a All Admissible Linear Estimators of a Multivariate Poisson Mean
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520			\|a 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.
540			\|a Copyright 1985 Institute of Mathematical Statistics
650		4	\|a Estimation
650		4	\|a multivariate Poisson parameter
650		4	\|a decision theory
650		4	\|a linear estimators
650		4	\|a admissibility
650		4	\|a linear models
650		4	\|a Mathematics \|x Applied mathematics \|x Statistics \|x Applied statistics \|x Inferential statistics \|x Statistical estimation \|x Estimation methods \|x Estimators
650		4	\|a Behavioral sciences \|x Psychology \|x Cognitive psychology \|x Cognitive processes \|x Decision making \|x Bayesian theories \|x Bayes estimators
650		4	\|a Mathematics \|x Pure mathematics \|x Geometry \|x Coordinate systems
650		4	\|a Mathematics \|x Pure mathematics \|x Linear algebra \|x Matrix theory \|x Matrices
650		4	\|a Information science \|x Information analysis \|x Data analysis \|x Regression analysis \|x Linear regression \|x Least squares
650		4	\|a Information science \|x Information analysis \|x Data analysis \|x Regression analysis \|x Linear regression \|x Linear models
650		4	\|a Mathematics \|x Pure mathematics \|x Discrete mathematics \|x Number theory \|x Numbers \|x Real numbers \|x Rational numbers \|x Integers
650		4	\|a Mathematics \|x Pure mathematics \|x Probability theory \|x Random variables
650		4	\|a Mathematics \|x Applied mathematics \|x Statistics \|x Statistical theories \|x Estimation theory
650		4	\|a Philosophy \|x Logic \|x Metalogic \|x Logical truth \|x Sufficient conditions
655		4	\|a research-article
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912			\|a GBV_ILN_2061
912			\|a GBV_ILN_2088
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912			\|a GBV_ILN_4126
912			\|a GBV_ILN_4242
912			\|a GBV_ILN_4249
912			\|a GBV_ILN_4251
912			\|a GBV_ILN_4305
912			\|a GBV_ILN_4306
912			\|a GBV_ILN_4307
912			\|a GBV_ILN_4313
912			\|a GBV_ILN_4322
912			\|a GBV_ILN_4323
912			\|a GBV_ILN_4324
912			\|a GBV_ILN_4325
912			\|a GBV_ILN_4326
912			\|a GBV_ILN_4335
912			\|a GBV_ILN_4338
912			\|a GBV_ILN_4346
912			\|a GBV_ILN_4367
912			\|a GBV_ILN_4393
912			\|a GBV_ILN_4700
951			\|a AR
952			\|d 13 \|j 1985 \|e 1 \|h 282-294