Bayesian analysis for quantile smoothing spline  

作　　者：Zhongheng Cai Dongchu Sun 

机构地区：[1]Faculty of Economics and Management,School of Statistics,East China Normal University,Shanghai,People's Republic of China [2]Department of Statistics,University of Nebraska-Lincoln,Lincoln,NE,USA

出　　处：《Statistical Theory and Related Fields》2021年第4期346-364,共19页统计理论及其应用（英文）

基　　金：The project was supported by the National Natural Science Foundation of China[Grant Number 11671146].

摘　　要：In Bayesian quantile smoothing spline[Thompson,P.,Cai,Y.,Moyeed,R.,Reeve,D.,&Stander,J.(2010).Bayesian nonparametric quantile regression using splines.Computational Statistics and Data Analysis,54,1138-1150.],a fixed-scale parameter in the asymmetric Laplace likelihood tends to result in misleading fitted curves.To solve this problem,we propose a new Bayesian quantile smoothing spline(NBQSS),which considers a random scale parameter.To begin with,we justify its objective prior options by establishing one sufficient and one necessary condition of the posterior propriety under two classes of general priors including the invariant prior for the scale component.We then develop partially collapsed Gibbs sampling to facilitate the compu-tation.Out of a practical concern,we extend the theoretical results to NBQSS with unobserved knots.Finally,simulation studies and two real data analyses reveal three main findings.Firstly,NBQSS usually outperforms other competing curve fitting methods.Secondly,NBQSS consid-ering unobserved knots behaves better than the NBQSS without unobserved knots in terms of estimation accuracy and precision.Thirdly,NBQSS is robust to possible outliers and could provide accurate estimation.

关 键 词：asymmetric Laplace likelihood objective Bayesian analysis posterior propriety quantile regression smoothing spline 

分 类 号：O17[理学—数学]