Identifiability of continuous mixtures of unknown Gaussian distributions. (English) Zbl 0588.60014

Bruni, C.; Koch, G.

Ann. Probab. 13, 1341-1357 (1985).

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.

MSC:

60E05	Probability distributions: general theory
45B05	Fredholm integral equations

Keywords:

Fredholm equations; identifiability of the mixing distribution; continuous mixture of Gaussian distributions