Adaptive Bayesian Estimation of Discrete‐Continuous Distributions Under Smoothness and Sparsity
研究了在异质光滑性条件下，对离散连续混合分布进行非参数估计，提出贝叶斯正态混合模型，其后验收缩率接近理论下界，在模拟中表现优异，适用于结构离散选择模型的第一阶段估计。
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.