Open Access
2010 Adaptive Bayesian density estimation with location-scale mixtures
Willem Kruijer, Judith Rousseau, Aad van der Vaart
Electron. J. Statist. 4: 1225-1257 (2010). DOI: 10.1214/10-EJS584


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.


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Willem Kruijer. Judith Rousseau. Aad van der Vaart. "Adaptive Bayesian density estimation with location-scale mixtures." Electron. J. Statist. 4 1225 - 1257, 2010.


Published: 2010
First available in Project Euclid: 8 November 2010

zbMATH: 1329.62188
MathSciNet: MR2735885
Digital Object Identifier: 10.1214/10-EJS584

Primary: 62G07 , 62G20

Keywords: Bayesian density estimation , Convergence rates , location-scale mixtures , Nonparametric density estimation , Rate-adaptive density estimation

Rights: Copyright © 2010 The Institute of Mathematical Statistics and the Bernoulli Society

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