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June, 1983 Natural Exponential Families with Quadratic Variance Functions: Statistical Theory
Carl N. Morris
Ann. Statist. 11(2): 515-529 (June, 1983). DOI: 10.1214/aos/1176346158


The normal, Poisson, gamma, binomial, negative binomial, and NEFGHS distributions are the six univariate natural exponential families (NEF) with quadratic variance functions (QVF). This sequel to Morris (1982) treats certain statistical topics that can be handled within this unified NEF-QVF formulation, including unbiased estimation, Bhattacharyya and Cramer-Rao lower bounds, conditional distributions and moments, quadratic regression, conjugate prior distributions, moments of conjugate priors and posterior distributions, empirical Bayes and $G_2$ minimax, marginal distributions and their moments, parametric empirical Bayes, and characterizations.


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Carl N. Morris. "Natural Exponential Families with Quadratic Variance Functions: Statistical Theory." Ann. Statist. 11 (2) 515 - 529, June, 1983.


Published: June, 1983
First available in Project Euclid: 12 April 2007

zbMATH: 0521.62014
MathSciNet: MR696064
Digital Object Identifier: 10.1214/aos/1176346158

Primary: 60E05
Secondary: 60E07 , 60F10 , 62E15 , 62E30

Keywords: $G_2$ minimax , Bayesian analysis , Bhattacharyya bounds , Binomial distribution , conjugate priors , exponential families , gamma distribution , natural exponential families , negative binomial distribution , NEG-GHS distribution , normal distribution , parametric empirical Bayes and characterizations , Poisson distribution , posteriror moments , quadratic regression , quadratic variance function , unbiased estimation

Rights: Copyright © 1983 Institute of Mathematical Statistics


Vol.11 • No. 2 • June, 1983
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