The Annals of Statistics

Exponential Family Mixture Models (with Least-Squares Estimators)

Bruce G. Lindsay

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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

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

First available in Project Euclid: 12 April 2007

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Primary: 62F10: Point estimation
Secondary: 62F20

Mixtures random effects exponential family weighted least squares


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

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