广西师范大学学报（自然科学版） ›› 2024, Vol. 42 ›› Issue (5): 117-129.doi: 10.16088/j.issn.1001-6600.2023102501

• 研究论文 • 上一篇    下一篇

部分线性变系数模型的贝叶斯复合分位数回归

李灿, 杨建波, 李荣*   

  1. 贵州民族大学 数据科学与信息工程学院,贵州 贵阳 550025
  • 收稿日期:2023-10-25 修回日期:2024-01-11 出版日期:2024-09-25 发布日期:2024-10-11
  • 通讯作者: 李荣(1980—),女(侗族),湖南怀化人,贵州民族大学副教授。E-mail: lirongjiewu@126.com
  • 基金资助:
    贵州省教育厅自然科学基金(黔教技〔2022〕015号);贵州省科技计划项目(黔科合基础〔2017〕1083号)

Bayesian Composite Quantile Regression for a Partially Linear Variable Coefficient Model

LI Can, YANG Jianbo, LI Rong*   

  1. School of Data Science and Information Engineering, Guizhou Minzu University, Guiyang Guizhou 550025, China
  • Received:2023-10-25 Revised:2024-01-11 Online:2024-09-25 Published:2024-10-11

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摘要： 部分线性变系数模型由参数和非参数2部分组成,具有适应范围广和解释性强双重优点。针对该模型的参数估计问题,采用B样条方法逼近非参数部分的未知光滑函数,进而利用复合非对称拉普拉斯分布实现贝叶斯复合分位数回归,并基于Gibbs抽样算法推导出所有未知参数的后验分布,以获取参数的估计值。通过数值模拟对贝叶斯复合分位数回归与贝叶斯分位数回归、贝叶斯线性回归参数估计效果进行比较分析,结果显示:当误差服从非正态分布时,在均方误差准则下,贝叶斯复合分位数回归估计表现更优。基于上述3种方法对实例数据进行预测分析,结果表明:在平均绝对偏差和均方误差预测意义下,基于贝叶斯复合分位数回归的预测效果更好。

关键词: 部分线性变系数模型, B样条, 贝叶斯复合分位数回归, 均方误差, Gibbs抽样算法

Abstract: The partial linear variable coefficient model consists of two parts,parameter and non-parameter,which has the advantages of wide range of adaptation and strong interpretation. To solve the parameter estimation problem of the model,the B-spline method is used to approximate the unknown smooth function of the non-parametric part,and then the compound asymmetric Laplacian distribution is used to realize the Bayesian composite quantile regression,and the posterior distribution of all the unknown parameters is derived based on the Gibbs sampling algorithm. Through numerical simulation,Bayesian compound quantile regression is compared with Bayesian quantile regression and Bayesian linear regression parameter estimation. The results show that when the error follows non-normal distribution,Bayesian compound quantile regression estimation performs better under mean square error criterion. Finally,based on the above three methods to predict the case data,the results show that in terms of mean absolute deviation and mean square error prediction,the prediction effect based on Bayesian compound quantile regression is the best.

Key words: partially linear variable coefficient model, B-spline, Bayesian composite quantile regression, mean square error, Gibbs sampling algorithm

中图分类号:  O212.1

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