Joint Estimation of Quantile Planes Over Arbitrary Predictor Spaces

作     者：Yang, Yun Tokdar, Surya T. 

作者机构：Duke Univ Stat Sci Box 90251 Durham NC 27708 USA 

出 版 物：《JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION》 (J. Am. Stat. Assoc.)

年 卷 期：2017年第112卷第519期

页      面：1107-1120页

核心收录：

学科分类：0202[经济学-应用经济学] 02[经济学] 020208[经济学-统计学] 07[理学] 0714[理学-统计学（可授理学、经济学学位）] 

基　　金：National Institute of Environmental Health Sciences (NIEHS) of the National Institutes of Health (NIH) [ES017436  R01ES020619] 

主　　题：Bayesian inference Bayesian nonparametric models Gaussian processes Joint quantile model Linear quantile regression 

摘      要：In spite of the recent surge of interest in quantile regression, joint estimation of linear quantile planes remains a great challenge in statistics and econometrics. We propose a novel parameterization that characterizes any collection of noncrossing quantile planes over arbitrarily shaped convex predictor domains in any dimension by means of unconstrained scalar, vector and function valued parameters. Statistical models based on this parameterization inherit a fast computation of the likelihood function, enabling penalized likelihood or Bayesian approaches to model fitting. We introduce a complete Bayesian methodology by using Gaussian process prior distributions on the function valued parameters and develop a robust and efficient Markov chain Monte Carlo parameter estimation. The resulting method is shown to offer posterior consistency under mild tail and regularity conditions. We present several illustrative examples where the new method is compared against existing approaches and is found to offer better accuracy, coverage and model fit. Supplementary materials for this article are available online.