Econometrica

Journal Of The Econometric Society

An International Society for the Advancement of Economic
Theory in its Relation to Statistics and Mathematics

Edited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262

Econometrica: May, 2022, Volume 90, Issue 3

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

https://doi.org/10.3982/ECTA17884
p. 1355-1377

Andriy Norets, Justinas Pelenis

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.


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Supplemental Material

Supplement to "Adaptive Bayesian Estimation of Discrete-Continuous Distributions under Smoothness and Sparsity"

Norets , Andriy, and Justinas Pelenis

This zip file contains the replication files for the manuscript.

Supplement to "Adaptive Bayesian Estimation of Discrete-Continuous Distributions under Smoothness and Sparsity"

Norets, Andriy, and Justinas Pelenis

This online appendix contains material not found within the manuscript.