Posterior contraction rates for deconvolution of Dirichlet-Laplace mixtures

Fengnan Gao; Aad van der Vaart

doi:10.1214/16-EJS1119

Electronic Journal of Statistics

Electron. J. Statist.
Volume 10, Number 1 (2016), 608-627.

Posterior contraction rates for deconvolution of Dirichlet-Laplace mixtures

Fengnan Gao and Aad van der Vaart

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Abstract

We study nonparametric Bayesian inference with location mixtures of the Laplace density and a Dirichlet process prior on the mixing distribution. We derive a contraction rate of the corresponding posterior distribution, both for the mixing distribution relative to the Wasserstein metric and for the mixed density relative to the Hellinger and $L_{q}$ metrics.

Article information

Source
Electron. J. Statist. Volume 10, Number 1 (2016), 608-627.

Dates
Received: July 2015
First available in Project Euclid: 4 March 2016

Permanent link to this document
http://projecteuclid.org/euclid.ejs/1457123508

Digital Object Identifier
doi:10.1214/16-EJS1119

Mathematical Reviews number (MathSciNet)
MR3471990

Zentralblatt MATH identifier
1332.62157

Subjects
Primary: 62G20: Asymptotic properties
Secondary: 62G05: Estimation

Keywords
Bayesian inference contraction rate Dirichlet process minimax rate Wasserstein metric

Citation

Gao, Fengnan; van der Vaart, Aad. Posterior contraction rates for deconvolution of Dirichlet-Laplace mixtures. Electron. J. Statist. 10 (2016), no. 1, 608--627. doi:10.1214/16-EJS1119. http://projecteuclid.org/euclid.ejs/1457123508.

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Posterior contraction rates for deconvolution of Dirichlet-Laplace mixtures

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