Exponential family mixture models (with least-squares estimators)
type: Item
instance of: scholarly article
title: Exponential family mixture models (with least-squares estimators)
zbMATH Open document ID: 0587.62057
published in: The Annals of Statistics
publication date: 1986-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 62F10
Mathematics Subject Classification ID: 62E10
Mathematics Subject Classification ID: 60E07
zbMATH DE Number: 3942742
zbMATH Keywords: several-parameter exponential family
zbMATH Keywords: random effects
zbMATH Keywords: one parameter exponential family density
zbMATH Keywords: mixing distribution
zbMATH Keywords: Reweighted infinitely divisible distributions
zbMATH Keywords: mixture of negative exponentials
zbMATH Keywords: linearity of the posterior mean
zbMATH Keywords: discrete case
zbMATH Keywords: least-squares estimators
zbMATH Keywords: Poisson example
author: Bruce G. Lindsay
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176349845
OpenAlex ID: W2003245616
DOI: 10.1214/AOS/1176349845
description: scientific article; zbMATH DE number 3942742