[1]王小刚,陈姜猛.基于光滑化方法的分段线性删失分位数回归模型估计[J].江西师范大学学报(自然科学版),2022,(03):268.[doi:10.16357/j.cnki.issn1000-5862.2022.03.09]
　WANG Xiaogang,CHEN Jiangmeng.The Piecewise Linear Censored Quantile Regression Model Estimation Based on Smoothing Technique[J].Journal of Jiangxi Normal University:Natural Science Edition,2022,(03):268.[doi:10.16357/j.cnki.issn1000-5862.2022.03.09]
点击复制

基于光滑化方法的分段线性删失分位数回归模型估计()
分享到：

《江西师范大学学报》（自然科学版）[ISSN:1006-6977/CN:61-1281/TN]

卷:
期数:
2022年03期
页码:
268
栏目:
数学与应用数学
出版日期:
2022-05-25

文章信息/Info

Title:
The Piecewise Linear Censored Quantile Regression Model Estimation Based on Smoothing Technique
文章编号:
1000-5862(2022)03-0268-09
作者:
王小刚; 陈姜猛
北方民族大学数学与信息科学学院,宁夏 银川 750021
Author(s):
WANG Xiaogang; CHEN Jiangmeng
School of Mathematics and Information Science,North Minzu University,Yinchuan Ningxia 750021,China
关键词:
光滑化方法;  分段线性;  删失分位数回归模型;  变点
Keywords:
smoothing tenchnique;  piecewise linear;  censored quantile regression model;  change point
分类号:
O 212.2
DOI:
10.16357/j.cnki.issn1000-5862.2022.03.09
文献标志码:
A
摘要:
针对在分段线性删失分位数回归模型中的变点问题,该文通过引入光滑化方法得到了变点位置及模型系数的估计,推导了参数估计的大样本性质.光滑化方法解决了在变点估计方法中常用的格点搜索法存在计算烦琐、解释意义不强的问题,弥补了线性化技术无法证明渐近性的不足,提高了估计的有效性和稳健性.蒙特卡罗模拟结果验证了在同方差和异方差、固定和随机删失下在不同分位点时的估计效果都具有有效性和稳健性.药物滥用数据的实证分析表明:复发时间间隔与治疗时间存在正向影响,且复发时间在0.498处存在变点(0.5分位数),治疗时间在0.498之前的复发时间间隔比在0.498之后的更长,即大约前一半时间的治疗更加有效.
Abstract:
The smoothing technique is proposed in the piecewise linear censored quantile regression model to solve the problem of change point,the estimator of change point and coefficients are obtained,and the large sample properties of the estimator is derived.The smoothing technique solves the cumbersome calculation and unreal meaning of the grid search method,and remedies the difficulty that linearization technology cannot prove the asymptotic properties.The validity and robustness of the estimation are verified by Monte Carlo simulation with homoscedasticity and heteroscedasticity,fixed and random censoring at different quantiles.The empirical analysis of drug abuse data shows that the recurrence interval and treatment time have a positive effect,and the recurrence time has a change point at 0.498(0.5 quantile).The treatment time before 0.498 is longer than after 0.498,that is,the treatment in the first half of the time is more effective.

参考文献/References:

[1] POWELL J L.Least absolute deviations estimation for the censored regression model[J].Journal of Econometrics,1984,25(3):303-325.
[2] PORTNOY S.Censored regression quantiles[J].Journal of American Statistical Association,2003,98(464):1001-1012.
[3] PENG Limin,HUANG Yijian.Survival analysis with quantile regression models[J].Journal of the American Statistical Association,2008,103(482):637-649.
[4] WANG Huixia Judy,WANG Lan.Locally weighted censored quantile regression[J].Journal of American Statistical Association,2009,104(487):1117-1128.
[5] TANG Yanlin,WANG Huixia Judy.Penalized regression across multiple quantiles under random censoring[J].Journal of Multivariate Analysis,2015,141:132-146.
[6] 张倩倩,郑茜,王纯杰,等.删失分位数回归在医疗费用中的应用[J].数理统计与管理,2018,37(6):1050-1062.
[7] 李忠桂,何书元.右删失数据下分位数回归的光滑经验似然检验[J].应用概率统计,2019,35(2):153-164.
[8] 孙桂萍,厉诚博,周勇.长度偏差右删失数据剩余寿命的分位数回归[J].数学学报(中文版),2020,63(1):1-18.
[9] 张立文,倪中新,何勇,等.删失分位数回归模型中的变点检测问题[J].中国科学:数学,2018,48(9):1159-1180.
[10] 王江峰,范国良,温利民.删失指标随机缺失下回归函数的复合分位数回归估计[J].系统科学与数学,2018,38(11):1347-1362.
[11] LERMAN P M.Fitting segmented regression models by grid search[J].Journal of the Royal Statistical Society:Series C(Applied Statistics),1980,29(1):77-84.
[12] LI Chenxi,WEI Ying,CHAPPEL R,et al.Bent line quantile regression with application to an allometric study of land mammals' speed and mass[J].Biometrics,2011,67(1):242-249.
[13] LI Dong,TONG H.Nested sub-sample search algorithm for estimation of threshold models[J].Statistica Sinica,2016,26(4):1543-1554.
[14] HOROWITZ J L.A smoothed maximum score estimator for the binary response model[J].Econometrica,1992,60(3):505-531.
[15] MUGGEO V M R.Estimating regression models with unknown break-points[J].Statistics in Medicine,2003,22(19):3055-3071.
[16] HIRUKAWA M.Asymmetric kernel smoothing:theory and applications in economics and finance[M].Singapore:Springer,2018:59-71.
[17] ZHOU Xiaoying,ZHANG Feipeng.Bent line quantile regression via a smoothing technique[J].Statistical Analysis and Data Mining,2020,13(3):216-228.
[18] 王小刚,李冰.基于核函数方法的逐段线性Tobit回归模型估计[J].山东大学学报(理学版),2020,55(6):1-9.
[19] HE Xuming,SHAO Qiman.A general Bahadur representation of M-estimators and its application to linear regression[J].The Annals of Statistics,1996,24(6):2608-2630.
[20] HENDRICKS W,KOEBKER R.Hierarchical spline models for conditional quantiles and the demand for electricity[J].Journal of the American Statistical Association,1992,87(417):58-68.
[21] HALL P,SHEATHER S J.On the distribution of a studentized quantile[J].Journal of the Royal Statistical Society:Series B(Methodological),1988,50(3):381-391.
[22] HOSMER DW,Jr,LEMESHOW S.Applied survival analysis:regression modeling of time to event data[M].New York:John Wiley & Sons,1999.
[23] KOENKER R.Censored quantile regression redux[J].Journal of Statistical Software,2008,27(6):1-25.

备注/Memo

备注/Memo:
收稿日期:2022-01-10
基金项目:宁夏自然科学基金(2021AAC03186),宁夏高等教育一流学科建设基金(NXYLXK2017B09)和北方民族大学服务宁夏九大产业(FWNX36)资助项目.
作者简介:王小刚(1980—),男,宁夏银川人,教授,博士,主要从事变点理论研究.E-mail:wxg@nun.edu.cn
更新日期/Last Update: 2022-05-25