A Data-Driven Bound on Variances for Avoiding Degeneracy in Univariate Gaussian Mixtures

@inproceedings{Biernacki2011ADB,
  title={A Data-Driven Bound on Variances for Avoiding Degeneracy in Univariate Gaussian Mixtures},
  author={Biernacki and Castellan},
  year={2011}
}
In the case of univariate 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. 

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