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

Author

Listed:
  • Norets, Andriy

    (Department of Economics, Brown University)

  • Pelenis, Justinas

    (Vienna 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.

Suggested Citation

  • Norets, Andriy & Pelenis, Justinas, 2018. "Adaptive Bayesian Estimation of Mixed Discrete-Continuous Distributions under Smoothness and Sparsity," Economics Series 342, Institute for Advanced Studies.
    • Handle: RePEc:ihs:ihsesp:342
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    File URL: https://irihs.ihs.ac.at/id/eprint/4711
    File Function: First version, 2018
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    Keywords

    Bayesian nonparametrics; adaptive rates; minimax rates; posterior contraction; discretecontinuous distribution; mixed scale; mixtures of normal distributions; latent variables;
    All these keywords.

    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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