The Annals of Statistics

Bayes Empirical Bayes Estimation for Natural Exponential Families with Quadratic Variance Functions

G. G. Walter and G. G. Hamedani

Full-text: Open access

Abstract

Certain orthogonal polynomials are employed to estimate the prior distribution of the parameter of natural exponential families with quadratic variance functions in an approach which combines Bayesian and nonparametric empirical Bayesian methods. These estimates are based on samples from the marginal distribution rather than the conditional distribution.

Article information

Source
Ann. Statist., Volume 19, Number 3 (1991), 1191-1224.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176348245

Digital Object Identifier
doi:10.1214/aos/1176348245

Mathematical Reviews number (MathSciNet)
MR1126321

Zentralblatt MATH identifier
0741.62006

JSTOR
links.jstor.org

Subjects
Primary: 60E05: Distributions: general theory
Secondary: 62F10: Point estimation 62F15: Bayesian inference

Keywords
Exponential families natural exponential families quadratic variance function normal distribution Poisson distribution gamma distribution binomial distribution negative binomial distribution hyperbolic secant distribution orthogonal polynomials moments

Citation

Walter, G. G.; Hamedani, G. G. Bayes Empirical Bayes Estimation for Natural Exponential Families with Quadratic Variance Functions. Ann. Statist. 19 (1991), no. 3, 1191--1224. doi:10.1214/aos/1176348245. https://projecteuclid.org/euclid.aos/1176348245


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