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• W2079638812 abstract "We consider Bayesian nonparametric density estimation using a Pitman-Yor or a normalized inverse-Gaussian process convolution kernel mixture as the prior distribution for a density. The procedure is studied from a frequentist perspective. Using the stick-breaking representation of the Pitman-Yor process and the finite-dimensional distributions of the normalized inverse-Gaussian process, we prove that, when the data are independent replicates from a density with analytic or Sobolev smoothness, the posterior distribution concentrates on shrinking Lp-norm balls around the sampling density at a minimax-optimal rate, up to a logarithmic factor. The resulting hierarchical Bayesian procedure, with a fixed prior, is adaptive to the unknown smoothness of the sampling density." @default.
• W2079638812 created "2016-06-24" @default.
• W2079638812 creator A5044127469 @default.
• W2079638812 date "2014-06-01" @default.
• W2079638812 modified "2023-09-27" @default.
• W2079638812 title "Adaptive Bayesian Density Estimation in Lp-metrics with Pitman-Yor or Normalized Inverse-Gaussian Process Kernel Mixtures" @default.
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• W2079638812 doi "https://doi.org/10.1214/14-ba863" @default.
• W2079638812 hasPublicationYear "2014" @default.
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