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

• 成果类型: Article
• 署名作者: Norets, Andriy; Pelenis, Justinas
• 署名单位: Brown University
• 刊物名称: ECONOMETRICA
• ISSN/ISSBN: 0012-9682
• DOI: 10.3982/ECTA17884
• 发表日期: 2022
• 页码: 1355-1377
• 关键词: nonparametric-estimation; DENSITY-ESTIMATION; CONVERGENCE; mixtures; rates; binary

摘要

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.