The Annals of Statistics

Exponential Family Mixture Models (with Least-Squares Estimators)

Bruce G. Lindsay

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Statist., Volume 14, Number 1 (1986), 124-137.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176349845

Digital Object Identifier
doi:10.1214/aos/1176349845

Mathematical Reviews number (MathSciNet)
MR829558

Zentralblatt MATH identifier
0587.62057

JSTOR
links.jstor.org

Subjects
Primary: 62F10: Point estimation
Secondary: 62F20

Keywords
Mixtures random effects exponential family weighted least squares

Citation

Lindsay, Bruce G. Exponential Family Mixture Models (with Least-Squares Estimators). Ann. Statist. 14 (1986), no. 1, 124--137. doi:10.1214/aos/1176349845. https://projecteuclid.org/euclid.aos/1176349845


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