Título:
A Cramér-Wold theorem for mixtures
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Autor:
Fraiman, Ricardo
Moreno, Leonardo
Ransford, Thomas
Moreno, Leonardo
Ransford, Thomas
Tutor:
Tipo de documento:
Preprint
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Palabras clave:
Descriptores:
GAUSSIAN DISTRIBUTION
T-DISTRIBUTION.
PROJECTION
IDENTIFIABILITY
T-DISTRIBUTION.
PROJECTION
IDENTIFIABILITY
Año de publicación:
2024
Contenido:
Resumen:
We show how a Cramér-Wold theorem for a family of multivariate probability distributions can be used to generate a similar theorem for mixtures (convex combinations) of distributions drawn from the same family. Using this abstract result, we establish a Cramér-Wold theorem for mixtures of multivariate Gaussian distributions. According to this theorem, two such mixtures can be distinguished by projecting them onto a certain predetermined finite set of lines, the number of lines depending only on the total number Gaussian distributions involved and on the ambient dimension. A similar result is also obtained for mixtures of multivariate t-distributions.
Descripción:
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arXiv
EN:
Mathematics (Probability), arXiv: 2410.22038v1, oct. 2024, pp.1-11
Financiadores:
ANII: FCE-3-2022-1-172289
Citación:
Fraiman, R, Moreno, L y Ransford, T. "A Cramér-Wold theorem for mixtures". [Preprint]. Publicado en: Mathematics (Probability). 2024, arXiv: 2410.22038v1, oct. 2024, pp. 1-11. DOI: 10.48550/arXiv.2410.22038
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Licencia:
Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0)
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| Ficheros | Descripción | Tamaño | Formato | ||
|---|---|---|---|---|---|
| 2410.22038v1.pdf | — | 165.83 KB | Adobe PDF |