部分线性变系数分位数模型的贝叶斯P-样条估计  

Bayesian P-spline estimation of partially linear variable coefficient quantile model

作　　者：杨飘 黄介武 YANG Piao;HUANG Jiewu(School of Data Science and Information Engineering,Guizhou Minzu University,Guiyang 550025,China)

机构地区：[1]贵州民族大学数据科学与信息工程学院,贵阳550025

出　　处：《智能计算机与应用》2025年第1期88-94,共7页Intelligent Computer and Applications

基　　金：贵州省教育厅自然科学研究项目(黔教技[2022]015号,黔教技[2023]061号,黔教技[2023]062号,黔教技[2023]012号)。

摘　　要：部分线性变系数模型是一类重要的半参数回归模型,针对该模型的参数估计问题,本文利用贝叶斯P-样条方法近似非参数部分的未知光滑函数,进而利用非对称拉普拉斯分布实现贝叶斯分位数回归,推导出所有未知参数的条件后验分布,通过Gibbs抽样和Metropolis-Hastings算法获得参数的估计值。通过数值模拟对贝叶斯P-样条方法与B-样条方法的估计效果进行比较分析,结果显示在均方误差和标准差准则下,贝叶斯P-样条方法在不同分位点上的估计效果更优。Partial linear variable coefficient model is an important semi-parametric regression model.For the parameter estimation problem of this model,the Bayesian P-spline method is utilized to approximate the unknown smooth function of the non-parametric part,and then the Bayesian quantile regression is implemented using the asymmetric Laplace distribution to derive the posterior distributions of all the unknown parameters in order to obtain the estimates of the parameters,the parameter estimates were obtained by Gibbs and Metropolis-Hastings algorithm.Meanwhile,the estimation effect of Bayesian P-spline method is compared and analyzed with B-spline method through numerical simulation,and the results show that the Bayesian P-spline method has better estimation effect at different quartiles under the mean square error and standard deviation criterion.

关 键 词：部分线性变系数模型 贝叶斯P-样条 B-样条 GIBBS抽样 均方误差 

分 类 号：O212.1[理学—概率论与数理统计]