Section: New Results

Degeneracy in multivariate Gaussian mixtures

Participant : Christophe Biernacki.

In the case of Gaussian mixtures, unbounded likelihood is an important theoretical and practical problem. Using the weak information that the latent sample size of each component has to be greater than the space dimension, we derive a simple non-asymptotic stochastic lower bound on variances. We prove also that maximizing the likelihood under this data-driven constraint leads to consistent estimates. This work has been presented to a conference [31] . This is a joint work with Gwënaelle Castellan.