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Adaptive Bayesian Estimation of 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 a possibly increasing number of support points for the discrete part of the distribution. For these settings, we derive lower bounds on the estimation rates. 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 (up to a log factor) optimal adaptive estimation of mixed discrete‐continuous distributions. The proposed model demonstrates excellent performance in simulations mimicking the first stage in the estimation of structural discrete choice models.

Suggested Citation

  • Andriy Norets & Justinas Pelenis, 2022. "Adaptive Bayesian Estimation of Discrete‐Continuous Distributions Under Smoothness and Sparsity," Econometrica, Econometric Society, vol. 90(3), pages 1355-1377, May.
    • Handle: RePEc:wly:emetrp:v:90:y:2022:i:3:p:1355-1377
    DOI: 10.3982/ECTA17884
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    References listed on IDEAS

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    1. Norets, Andriy, 2021. "Optimal Auxiliary Priors And Reversible Jump Proposals For A Class Of Variable Dimension Models," Econometric Theory, Cambridge University Press, vol. 37(1), pages 49-81, February.
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