Section: New Results

Degeneracy in multivariate Gaussian mixtures (complete data case)

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, a simple non-asymptotic stochastic lower bound on variances is derived. It is proved also that maximizing the likelihood under this data-driven constraint leads to consistent estimates. This work has been presented as an invited talk to the international workshop [28] and a paper for an international journal is been prepared.

This is a joined work with Gwënaelle Castellan of University of Lille.