安庆师范大学学报（自然科学版）2026，Vol.32Issue(2)：17-27,11.DOI:10.13757/j.cnki.cn34-1328/n.2026.02.003
变系数部分函数型贝叶斯复合分位数回归
Bayesian Composite Quantile Regression for Varying-Coefficient Partial Functional Linear Models
摘要
Abstract
To address the parameter function estimation in varying-coefficient partial functional linear models,where con-ventional methods lack robustness against outliers and heavy-tailed errors,this paper develops a Bayesian composite quantile regression approach.By integrating multi-quantile information,the proposed method enhances estimation accuracy and robust-ness in complex data scenarios.First,B-spline basis functions are employed to approximate the varying-coefficient functions,and the slope function undergoes spectral decomposition via the functional principal component basis,thereby transforming in-finite-dimensional functional estimation into finite-dimensional parameter estimation.Assuming that the errors follow a com-posite asymmetric Laplace distribution,we establish the Bayesian composite quantile regression framework and derive the joint posterior distribution of unknown parameters by incorporating prior distributions.Second,A Gibbs sampling algorithm is employed to generate posterior samples,and functional estimates are reconstructed via basis expansions.Numerical simula-tions demonstrate that,under various error distributions,the proposed Bayesian composite quantile regression method outper-forms traditional composite quantile regression in terms of.both root mean squared error and standard deviation criteria.Fur-thermore,real data modeling also exhibits superior estimation accuracy.关键词
变系数部分函数型线性模型/贝叶斯复合分位数回归/B样条基/函数型主成分基/Gibbs抽样算法Key words
varying-coefficient partial functional linear models/Bayesian composite quantile regression/B-spline basis/functional principal component basis/Gibbs sampling algorithm分类
数理科学引用本文复制引用
赵庭,李荣,雷启贵,李明艳..变系数部分函数型贝叶斯复合分位数回归[J].安庆师范大学学报（自然科学版）,2026,32(2):17-27,11.基金项目
贵州省教育厅自然科学研究项目(黔教技[2022]015号)和贵州省高等学校大数据分析与智能计算重点实验室项目(黔教技[2023]012号) （黔教技[2022]015号）
