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

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  • Andriy Norets
  • Justinas Pelenis

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.

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  • Andriy Norets & Justinas Pelenis, 2018. "Adaptive Bayesian Estimation of Mixed Discrete-Continuous Distributions under Smoothness and Sparsity," Papers 1806.07484, arXiv.org.
    • Handle: RePEc:arx:papers:1806.07484
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    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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