Section: New Results

Degeneracy in 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. Currently, such results are proved in the univariate case [34] . The challenge is now not only to extend them in the multivariate situation but also to complete these theoretical results with some practical strategies for properly avoiding degeneracy in softwares devoted to such mixture estimations.

This is a joined work with Gwënaelle Castellan.