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.

Rates for Bayesian estimation of location-scale mixtures of super-smooth densities

SCRICCIOLO, CATIA
2016

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.
9783319272740
9783319272726
Alleva, Giorgio; Giommi, Andraea
Topics in theoretical and applied statistics
Scricciolo, Catia
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11565/3954324
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