A Bayesian Nonparametric Approach to Inference for Quantile Regression
提出一种贝叶斯非参数方法，通过狄利克雷过程混合模型对响应和协变量的联合分布建模，从条件响应分布中推断分位数曲线，并扩展至Tobit分位数回归处理部分缺失响应。
We develop a Bayesian method for nonparametric model–based quantile regression. The approach involves flexible Dirichlet process mixture models for the joint distribution of the response and the covariates, with posterior inference for different quantile curves emerging from the conditional response distribution given the covariates. An extension to allow for partially observed responses leads to a novel Tobit quantile regression framework. We use simulated data sets and two data examples from the literature to illustrate the capacity of the model to uncover nonlinearities in quantile regression curves, as well as nonstandard features in the response distribution.