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。
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 nonparametric 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.
作者
李灿
杨建波
李荣
LI Can;YANG Jianbo;LI Rong(School of Data Science and Information Engineering,Guizhou Minzu University,Guiyang Guizhou 550025,China)
出处
《广西师范大学学报（自然科学版）》
CAS
北大核心
2024年第5期117-129,共13页
Journal of Guangxi Normal University:Natural Science Edition
基金
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)。
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
partially linear variable coefficient model
B-spline
Bayesian composite quantile regression
mean square error
Gibbs sampling algorithm
