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

Norets, Andriy and Pelenis, Justinas (July 2018) Adaptive Bayesian Estimation of Mixed Discrete-Continuous Distributions under Smoothness and Sparsity. Former Series > Working Paper Series > IHS Economics Series 342, 34 p.

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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.

Item Type:	IHS Series
Keywords:	Bayesian nonparametrics, adaptive rates, minimax rates, posterior contraction, discretecontinuous distribution, mixed scale, mixtures of normal distributions, latent variables
Classification Codes (e.g. JEL):	C11, C14
Research Units:	Former Research Units (until 2020) > Macroeconomics and Economic Policy
Date Deposited:	08 Aug 2018 07:51
Last Modified:	27 Sep 2019 06:03
ISSN:	1605-7996
URI:	https://irihs.ihs.ac.at/id/eprint/4711

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