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

PDF (PC)

56

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

[1] ZHANG W Y,LEE S Y,SONG X Y. Local polynomial fitting in semivarying coefficient model[J]. Journal of Multivariate Analysis,2002,82(1):166-188. DOI: 10.1006/jmva.2001.2012.
[2] FAN J,HUANG T. Profile likelihood inferences on semiparametric varying-coefficient partially linear models[J]. Bernoulli,2005,11(6):1031-1057. DOI: 10.3150/bj/1137421639.
[3] HU X M,WANG Z Z,ZHAO Z W. Empirical likelihood for semiparametric varying-coefficient partially linear errors-in-variables models[J]. Statistics & Probability Letters,2009,79(8):1044-1052. DOI: 10.1016/j.spl.2008.12.011.
[4] SUN H,LIU Q. Robust empirical likelihood inference for partially linear varying coefficient models with longitudinal data[J]. Journal of Statistical Computation and Simulation,2023,93(10):1559-1579. DOI: 10.1080/00949655.2022.2145289.
[5] KOENKER R,BASSETT G JR.Regression quantiles[J]. Econometrica: Journal of the Econometric Society,1978:33-50. DOI: 10.2307/1913643.
[6] BO K,LI R Z,ZOU H. New efficient estimation and variable selection methods for semiparametric varing-coefficient partially linear models[J]. Annals of Statistics,2011,39(1):305-332. DOI: 10.1214/10-AOS842.
[7] YANG J,LU F,YANG H. Quantile regression for robust inference on varying coefficient partially nonlinear models[J]. Journal of the Korean Statistical Society,2018,47(2):172-184. DOI: 10.1016/j.jkss.2017.12.002.
[8] 田镇滔,张军舰.基于分位数方法的超高维删失数据的特征筛选[J].广西师范大学学报(自然科学版),2021,39(6):99-111. DOI: 10.16088/j.issn.1001-6600.2020122406.
[9] WANG B H,LIANG H Y. Quantile regression of ultra-high dimensional partially linear varying-coefficient model with missing observations[J]. Acta Mathematica Sinica: English Series,2023,39(9):1701-1726. DOI: 10.1007/S10114-023-0667-3.
[10] ZOU H,YUAN M. Composite quantile regression and the oracle model selection theory[J]. The Annals of Statistics,2008,36(3):1108-1126. DOI: 10.1214/07-AOS507.
[11] ZHANG R Q,LV Y Z,ZHAO W H,et al. Composite quantile regression and variable selection in single-index coefficient model[J]. Journal of Statistical Planning and Inference,2016,176:1-21. DOI: 10.1016/j.jspi.2016.04.003.
[12] JIN J,HAO C Y,MA T F. B-spline estimation for partially linear varying coefficient composite quantile regression models[J]. Communications in Statistics-Theory and Methods,2019,48(21):5322-5335. DOI: 10.1080/03610926.2018.1510006.
[13] 刘艳霞,芮荣祥,田茂再. 部分线性变系数模型的新复合分位数回归估计[J]. 应用数学学报,2021,44(2):159-174. DOI: 10.12387/C2021012.
[14] ZOU Y,FAN G,ZHANG R. Composite quantile regression for heteroscedastic partially linear varying-coefficient models with missing censoring indicators[J]. Journal of Statistical Computation and Simulation,2023,93(3):341-365. DOI: 10.1080/00949655.2022.2108030.
[15] HUANG H W,CHEN Z X. Bayesian composite quantile regression[J]. Journal of Statistical Computation and Simulation,2015,85(18):3744-3754. DOI: 10.1080/00949655.2015.1014372.
[16] TIAN Y Z,LIAN H,TIAN M Z. Bayesian composite quantile regression for linear mixed-effects models[J]. Communications in Statistics-Theory and Methods,2017,46(15):7717-7731. DOI: 10.1080/03610926.2016.1161798.
[17] ALHUSSEINIl F H H,GEORGESCU V. Bayesian composite Tobit quantile regression[J]. Journal of Applied Statistics,2018,45(4):727-739. DOI: 10.1080/02664763.2017.1299697.
[18] TIAN Y Z, WANG L Y, WU X Q. et al. Gibbs sampler algorithm of Bayesian weighted composite quantile regression[J]. Chinese Journal of Applied Probability and Statistics, 2019, 35(2): 178-192. DOI: 10.3969/j.issn.1001-4268.2019.02.006.
[19] 张永霞,田茂再. 基于贝叶斯的部分线性单指标复合分位回归的研究及其应用[J]. 系统科学与数学,2021,41(5):1381-1399. DOI: 10.12341/jssms20418.
[20] YUAN X H,XIANG X F,ZHANG X R. Bayesian composite quantile regression for the single-index model[J]. Plos One,2023,18(5):e0285277. DOI: 10.1371/JOURNAL.PONE.0285277.
[21] ALHAMZAWI R. Bayesian analysis of composite quantile regression[J]. Statistics in Biosciences,2016,8(2):358-373. DOI: 10.1007/s12561-016-9158-8.
[22] KOZUMI H,KOBAYASHI G. Gibbs sampling methods for Bayesian quantile regression[J]. Journal of Statistical Computation and Simulation,2011,81(11):1565-1578. DOI: 10.1080/00949655.2010.496117.
[23] TIAN R Q,XU D K,DU J,et al. Bayesian estimation for partially linear varying coefficient spatial autoregressive models[J]. Statistics and Its Interface,2022,15(1):105-113. DOI: 10.4310/21-SII682.
[24] BARNDORFF-NIELSEN O E,SHEPHARD N. Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics[J]. Journal of the Royal Statistical Society:Series B (Statistical Methodology),2001,63(2):167-241. DOI: 10.1111/1467-9868.00282.
[25] HE X M,FUNG W K,ZHU Z Y. Robust estimation in generalized partial linear models for clustered data[J]. Journal of the American Statistical Association,2005,100(472):1176-1184. DOI: 10.1198/016214505000000277.
[26] JIANG R,QIAN W M,ZHOU Z G. Weighted composite quantile regression for partially linear varying coefficient models[J]. Communications in Statistics: Theory and Methods,2018,47(16):3987-4005. DOI: 10.1080/03610926.2017.1366522.
[1] 赵婷婷, 杨凤莲. Laplace方程柯西问题的B样条方法[J]. 广西师范大学学报（自然科学版）, 2023, 41(3): 118-129.
[2] 舒婷, 罗幼喜, 李翰芳. 面板数据贝叶斯双惩罚分位回归方法研究[J]. 广西师范大学学报（自然科学版）, 2022, 40(1): 150-165.
[3] 武康康, 周鹏, 陆叶, 蒋丹, 闫江鸿, 钱正成, 龚闯. 基于小批量梯度下降法的FIR滤波器[J]. 广西师范大学学报（自然科学版）, 2021, 39(4): 9-20.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
[1] 李文博, 董青, 刘超, 张奇. 基于对比学习的儿科问诊对话细粒度意图识别[J]. 广西师范大学学报（自然科学版）, 2024, 42(4): 1 -10 .
[2] 高盛祥, 杨元樟, 王琳钦, 莫尚斌, 余正涛, 董凌. 面向域外说话人适应场景的多层级解耦个性化语音合成[J]. 广西师范大学学报（自然科学版）, 2024, 42(4): 11 -21 .
[3] 朱格格, 黄安书, 覃盈盈. 基于Web of Science的国际红树林研究发展态势分析[J]. 广西师范大学学报（自然科学版）, 2024, 42(5): 1 -12 .
[4] 何静, 冯元柳, 邵靖雯. 基于CiteSpace的多源数据融合研究进展[J]. 广西师范大学学报（自然科学版）, 2024, 42(5): 13 -27 .
[5] 左钧元, 李欣彤, 曾子涵, 梁超, 蔡进军. 金属有机骨架基催化剂在糠醛选择性加氢反应中的应用研究进展[J]. 广西师范大学学报（自然科学版）, 2024, 42(5): 28 -38 .
[6] 谭全伟, 薛贵军, 谢文举. 基于VMD和RDC-Informer的短期供热负荷预测模型[J]. 广西师范大学学报（自然科学版）, 2024, 42(5): 39 -51 .
[7] 刘畅平, 宋树祥, 蒋品群, 岑明灿. 基于开关电容的差分无源N通道滤波器[J]. 广西师范大学学报（自然科学版）, 2024, 42(5): 52 -60 .
[8] 王党树, 孙龙, 董振, 贾如琳, 杨黎康, 吴家驹, 王新霞. 变化负载下全桥LLC谐振变换器参数优化设计[J]. 广西师范大学学报（自然科学版）, 2024, 42(5): 61 -71 .
[9] 张锦忠, 韦笃取. PMSM混沌系统无初始状态约束的固定时间有界控制[J]. 广西师范大学学报（自然科学版）, 2024, 42(5): 72 -78 .
[10] 涂智荣, 凌海英, 李帼, 陆声链, 钱婷婷, 陈明. 基于改进YOLOv7-Tiny的轻量化百香果检测方法[J]. 广西师范大学学报（自然科学版）, 2024, 42(5): 79 -90 .
版权所有 © 广西师范大学学报（自然科学版）编辑部
地址：广西桂林市三里店育才路15号　邮编：541004
电话：0773-5857325　E-mail: gxsdzkb@mailbox.gxnu.edu.cn
本系统由北京玛格泰克科技发展有限公司设计开发