Entropies and Rates of Convergence for Maximum Likelihood and Bayes Estimation for Mixtures of Normal Densities

@inproceedings{Ghosal2001EntropiesAR,
  title={Entropies and Rates of Convergence for Maximum Likelihood and Bayes Estimation for Mixtures of Normal Densities},
  author={Subhashis Ghosal and Aad van der Vaart},
  year={2001}
}
We study the rates of convergence of the maximum likelihood estimator (MLE) and posterior distribution in density estimation problems, where the densities are location or location-scale mixtures of normal distributions with the scale parameter lying between two positive numbers. The true density is also assumed to lie in this class with the true mixing distribution either compactly supported or having sub-Gaussian tails. We obtain bounds for Hellinger bracketing entropies for this class, and… CONTINUE READING
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