Open Access
November, 1985 Identifiability of Continuous Mixtures of Unknown Gaussian Distributions
C. Bruni, G. Koch
Ann. Probab. 13(4): 1341-1357 (November, 1985). DOI: 10.1214/aop/1176992817


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.


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C. Bruni. G. Koch. "Identifiability of Continuous Mixtures of Unknown Gaussian Distributions." Ann. Probab. 13 (4) 1341 - 1357, November, 1985.


Published: November, 1985
First available in Project Euclid: 19 April 2007

zbMATH: 0588.60014
MathSciNet: MR806230
Digital Object Identifier: 10.1214/aop/1176992817

Primary: 60E05
Secondary: 45B05

Keywords: Fredholm equations , Identifiability of measures , mixture of Gaussian distributions

Rights: Copyright © 1985 Institute of Mathematical Statistics

Vol.13 • No. 4 • November, 1985
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