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EnglishWe consider Bayesian nonparametric density estimation with a Dirichlet process kernel mixture as a prior on the class of Lebesgue univariate densities, the emphasis being on the achievability of the error rate n^{-1/2}, up to a logarithmic factor, depending upon the kernel. We derive rates of convergence for the Bayes' estimator of super-smooth densities that are location-scale mixtures of densities whose Fourier transforms have sub-exponential tails. We show that a nearly parametric rate is attainable in the L^1-norm, under weak assumptions on the tail decay of the true mixing distribution and the overall Dirichlet process base measure.
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| Titolo: | Rates for Bayesian estimation of location-scale mixtures of super-smooth densities | |
| Data di pubblicazione: | 2016 | |
| Autori: | ||
| Autori: | Scricciolo, Catia | |
| Titolo del libro: | Topics in theoretical and applied statistics | |
| Tutti i curatori: | Alleva, Giorgio; Giommi, Andraea | |
| ISBN: | 9783319272740 9783319272726 | |
| Abstract: | We consider Bayesian nonparametric density estimation with a Dirichlet process kernel mixture as a prior on the class of Lebesgue univariate densities, the emphasis being on the achievability of the error rate n^{-1/2}, up to a logarithmic factor, depending upon the kernel. We derive rates of convergence for the Bayes' estimator of super-smooth densities that are location-scale mixtures of densities whose Fourier transforms have sub-exponential tails. We show that a nearly parametric rate is attainable in the L^1-norm, under weak assumptions on the tail decay of the true mixing distribution and the overall Dirichlet process base measure. | |
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1007/978-3-319-27274-0_5 | |
| Appare nelle tipologie: | 20 - Contributions to volume, chapters or articles / Contributo in volume, capitolo o saggio scientifico |
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| File | Descrizione | Tipologia | Licenza | |
|---|---|---|---|---|
| SIS 2012-Accepted paper.pdf | Documento in Pre-print (Pre-print document) | NON PUBBLICO - Accesso privato/ristretto | Administrator Richiedi una copia | |
| Editor Letter of Definitive Acceptance.pdf | Altro materiale allegato | NON PUBBLICO - Accesso privato/ristretto | Administrator Richiedi una copia |
http://hdl.handle.net/11565/3954324
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