Abstract
We study convergence rates of Bayesian density estimators based on finite location-scale mixtures of exponential power distributions. We construct approximations of β-Hölder densities be continuous mixtures of exponential power distributions, leading to approximations of the β-Hölder densities by finite mixtures. These results are then used to derive posterior concentration rates, with priors based on these mixture models. The rates are minimax (up to a logn term) and since the priors are independent of the smoothness the rates are adaptive to the smoothness.
Citation
Willem Kruijer. Judith Rousseau. Aad van der Vaart. "Adaptive Bayesian density estimation with location-scale mixtures." Electron. J. Statist. 4 1225 - 1257, 2010. https://doi.org/10.1214/10-EJS584
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