Identifiability of continuous mixtures of unknown Gaussian distributions
type: Item
instance of: scholarly article
title: Identifiability of continuous mixtures of unknown Gaussian distributions
zbMATH Open document ID: 0588.60014
published in: The Annals of Probability
publication date: 1985-01-01T00:00:00Z
review text: The problem of the identifiability of the mixing distribution and of the unknown parameters for a continuous mixture of Gaussian distributions is considered. Relevance of the problem under various analytical, statistical, and applicative points of view is stressed. Uniqueness of the mixing distribution and of the mean and variance functions for the mixed Gaussian distribution is proved. Furthermore, their continuous dependence on the mixture itself is proved under suitable topologies. These results also extend to the multidimensional case and to the case of non-Gaussian distributions, and/or signed mixing measure.
Mathematics Subject Classification ID: 60E05
Mathematics Subject Classification ID: 45B05
zbMATH DE Number: 3944940
zbMATH Keywords: Fredholm equations
zbMATH Keywords: identifiability of the mixing distribution
zbMATH Keywords: continuous mixture of Gaussian distributions
author: C. Bruni
author: G. Koch
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176992817
OpenAlex ID: W2094541826
DOI: 10.1214/AOP/1176992817
description: scientific article; zbMATH DE number 3944940