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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: | 9999 |
| Autori: | |
| Autori: | Scricciolo, Catia |
| Titolo del libro: | Springer volume of the international Series "Studies in Theoretical and Applied Statistics" |
| Tutti i curatori: | . |
| ISBN: | XXXXXXXXXX |
| 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. |
| Appare nelle tipologie: | 20 - Contributions to volume, chapters or articles / Contributo in volume Capitolo o Saggio Scientifico |
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