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March, 1986 Exponential Family Mixture Models (with Least-Squares Estimators)
Bruce G. Lindsay
Ann. Statist. 14(1): 124-137 (March, 1986). DOI: 10.1214/aos/1176349845


For an arbitrary one parameter exponential family density it is shown how to construct a mixing distribution (prior) on the parameter in such a way that the resulting mixture distribution is a two (or more) parameter exponential family. Reweighted infinitely divisible distributions are shown to be the parametric mixing distributions for which this occurs. As an illustration conditions are given under which a parametric mixture of negative exponentials is in the exponential family. Properties of the posterior are given, including linearity of the posterior mean in the natural parameter. For the discrete case a class of simply-computed yet fully-efficient least-squares estimators is given. A Poisson example is used to demonstrate the strengths and weaknesses of the approach.


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Bruce G. Lindsay. "Exponential Family Mixture Models (with Least-Squares Estimators)." Ann. Statist. 14 (1) 124 - 137, March, 1986.


Published: March, 1986
First available in Project Euclid: 12 April 2007

zbMATH: 0587.62057
MathSciNet: MR829558
Digital Object Identifier: 10.1214/aos/1176349845

Primary: 62F10
Secondary: 62F20

Rights: Copyright © 1986 Institute of Mathematical Statistics


Vol.14 • No. 1 • March, 1986
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