文章基本信息

标题：Adaptive density estimation based on a mixture of Gammas
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作者：Natalia Bochkina ; Judith Rousseau
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2017
卷号：11
期号：1
页码：916-962
DOI：10.1214/17-EJS1247
语种：English
出版社：Institute of Mathematical Statistics
摘要：We consider the problem of Bayesian density estimation on the positive semiline for possibly unbounded densities. We propose a hierarchical Bayesian estimator based on the gamma mixture prior which can be viewed as a location mixture. We study convergence rates of Bayesian density estimators based on such mixtures. We construct approximations of the local Hölder densities, and of their extension to unbounded densities, to be continuous mixtures of gamma distributions, leading to approximations of such 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 log n term) and since the priors are independent of the smoothness, the rates are adaptive to the smoothness.