A Cramér-Wold theorem for mixtures
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.
| 2024 | |
| ANII: FCE-3-2022-1-172289 | |
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GAUSSIAN DISTRIBUTION T-DISTRIBUTION. PROJECTION IDENTIFIABILITY |
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| Inglés | |
| Universidad de la República | |
| COLIBRI | |
| https://hdl.handle.net/20.500.12008/48465 | |
| Acceso abierto | |
| Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
