A Natural Identity for Exponential Families with Applications in Multiparameter Estimation

Hudson, H. Malcolm

doi:10.1214/aos/1176344194

Cited by 206 publications

(127 citation statements)

References 6 publications

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“…The proof is the same as in Hudson (1978) and Hwang (1982) and is omitted here. From this lemma with m = −1 and g(x 1 , x 2 ) ≡ 1, δ ML is found to be the uniformly minimum variance unbiased estimator (UMVUE) of λ.…”

Section: Estimation Of the Means In The Multiplicative Poisson Model mentioning

confidence: 99%

“…Hwang (1982) extended their results to the estimation of the mean parameters of a subclass of discrete exponential families. He generalized the identity of Hudson (1978) and derived an unbiased estimator of the difference of two risk functions. Chou (1991) gave a class of improved estimators for a wider class of discrete exponential families.…”

Section: Introductionmentioning

confidence: 99%

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Simultaneous Estimation of the Means in Some Poisson Log Linear Models

Hara

Takemura

2006

JJSS

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In this article we study the simultaneous estimation of the Poisson means in J-way multiplicative models and a decomposable model for three-way layouts. The estimators which improve on the maximum likelihood estimators under the normalized squared error losses are provided for each model. The proposed estimators correspond to the ones by Clevenson and Zidek (1975), Tsui and Press (1982) and Chou (1991).

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Section: Estimation Of the Means In The Multiplicative Poisson Model mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Simultaneous Estimation of the Means in Some Poisson Log Linear Models

Hara

Takemura

2006

JJSS

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“…When the distribution of X belongs to exponential family, the identity (2.2) reduces to the moment identity given by Hudson (1978).…”

Section: Generalized Stein's Identitymentioning

confidence: 99%

“…And it has been widely exploited since; it is discussed with some members of certain families of distributions Inspired from Stein, Hudson (1978) obtained an identity for the exponential family of distributions and studied its uses in multi parameter estimation. Prakasa Rao (1979) characterized the exponential family of distributions using the identity given by Hudson (1978), and then †Author E-mail: skkattu@yahoo.co.in.…”

Section: Introductionmentioning

confidence: 99%

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On Stein’s identity and its applications

Kattumannil

2009

Statistics & Probability Letters

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Abstract. Stein's identity and its role in inference procedures have been discussed widely in literature. We extend the identity to a general framework using an absolutely continuous function g(x) that characterizes the probability distributions. It is shown that some of the identities available in the literature are special cases of the proposed one. Further, we also discuss various applications of the proposed identity.

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Shrinkage Estimation

Casella¹

2005

Encyclopedia of Biostatistics

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Shrinkage estimation developed from the work of Stein for the estimation of the mean of a multivariate normal distribution. The observed vector is, from a decision theory viewpoint, inadmissible. The James–Stein estimator shrinks the observations toward zero. Later work involves estimators shrunk toward the sample mean. Shrinkage estimators are, however, not dominant in problems with a finite sample space, such as the binomial distribution. There are connections with Bayesian and empirical Bayes solutions.

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A Natural Identity for Exponential Families with Applications in Multiparameter Estimation

Cited by 206 publications

References 6 publications

Simultaneous Estimation of the Means in Some Poisson Log Linear Models

Simultaneous Estimation of the Means in Some Poisson Log Linear Models

On Stein’s identity and its applications

Shrinkage Estimation

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