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.File | Dimensione | Formato | |
---|---|---|---|
SIS 2012-Accepted paper.pdf
non disponibili
Tipologia:
Documento in Pre-print (Pre-print document)
Licenza:
NON PUBBLICO - Accesso privato/ristretto
Dimensione
152.11 kB
Formato
Adobe PDF
|
152.11 kB | Adobe PDF | Visualizza/Apri |
Editor Letter of Definitive Acceptance.pdf
non disponibili
Tipologia:
Altro materiale allegato
Licenza:
NON PUBBLICO - Accesso privato/ristretto
Dimensione
50.93 kB
Formato
Adobe PDF
|
50.93 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.