Adaptive Bayesian Estimation of Mixed Discrete-Continuous Distributions under Smoothness and Sparsity

Andriy Norets and Justinas Pelenis

No 342, Economics Series from Institute for Advanced Studies

Abstract: We consider nonparametric estimation of a mixed discrete-continuous distribution under anisotropic smoothness conditions and possibly increasing number of support points for the discrete part of the distribution. For these settings, we derive lower bounds on the estimation rates in the total variation distance. Next, we consider a nonparametric mixture of normals model that uses continuous latent variables for the discrete part of the observations. We show that the posterior in this model contracts at rates that are equal to the derived lower bounds up to a log factor. Thus, Bayesian mixture of normals models can be used for optimal adaptive estimation of mixed discrete-continuous distributions.

Keywords: Bayesian nonparametrics; adaptive rates; minimax rates; posterior contraction; discretecontinuous distribution; mixed scale; mixtures of normal distributions; latent variables (search for similar items in EconPapers)
JEL-codes: C11 C14 (search for similar items in EconPapers)
Pages: 34 pages
Date: 2018-07
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https://irihs.ihs.ac.at/id/eprint/4711 First version, 2018 (application/pdf)

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Working Paper: Adaptive Bayesian Estimation of Mixed Discrete-Continuous Distributions under Smoothness and Sparsity (2018)
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