删失部分线性可加模型的复合分位数回归及应用  

Composite Quantile Regression for Partially Linear Additive Model with Censored Responses and Its Application

作　　者：杨晓蓉[1,2] 李路 武皓月 许文婷 YANG Xiaorong;LI Lu;WU Haoyue;XU Wenting(School of Statistics and Mathematics,Zhejiang Gongshang University,Hangzhou,310018,China;Collaborative Innovation Center of Statistical Data Engineering Technology and Application Zhejiang Gongshang University,Hangzhou,310018,China)

机构地区：[1]浙江工商大学统计与数学学院,杭州310018 [2]浙江工商大学统计数据工程技术与应用协同创新中心,杭州310018

出　　处：《应用概率统计》2023年第4期604-622,共19页Chinese Journal of Applied Probability and Statistics

基　　金：浙江省自然科学基金项目(批准号:LY22A010006);国家社会科学基金项目(批准号:17BTJ027);浙江省重点建设高校优势特色学科(浙江工商大学统计学);浙江工商大学统计数据工程技术与应用协同创新中心;浙江省属高校基本业务费专项基金资助

摘　　要：本文针对一种具有广泛适用性的半参数模型,部分线性可加模型,研究其响应变量存在删失数据时模型系数和非参数函数的估计.对此,提出了一种基于数据增广的复合分位数回归估计方法.该方法利用分位数回归和分布函数之间的联系,构造插补数据集,并通过迭代采用复合分位数回归得到最终的估计值.所提方法放宽了对模型的假设,不但对迭代初始值的要求很低,还允许响应变量同时存在多种类型的删失,具有一定的普适性.数值模拟表明所提方法可以较为准确地估计出删失部分线性可加模型的系数和非参数函数.实证研究中,本文选取了北京市空气质量数据,测度了PM10浓度、CO浓度、温度、气压以及露点对PM2.5浓度的影响.结果显示,部分线性可加模型的复合分位数回归可以较好地从线性和非线性关系两个角度来刻画这些因素对PM2.5浓度的影响,并且所提方法在删失数据的处理上表现良好.In this paper,for a widely applicable semi-parametric model,partially linear additive model,we study the estimation of its coefficients and nonparametric functions when responses are censored.For this,a composite quantile regression estimation method based on data augmentation is proposed.This method utilizes the relationship between quantile regression and distribution function to construct the imputation dataset,and the final estimators are obtained by composite quantile regression through iterations.The proposed method relaxes the assumptions of the model,not only has low requirements for initial values of iterations but also allows the case when different types of censoring are present in the same dataset.Numerical simulations show that the proposed method can accurately estimate the coefficients and nonparametric functions of the censored partially linear additive model.In real data analysis,this paper studies the air quality in Beijing,and measures the effects of PM10 concentration,CO concentration,temperature,air pressure,and dew point on PM2.5 concentration.The results show that the composite quantile regression of the partially linear additive model can describe well the influence of these factors on PM2.5 from the perspective of linear and nonlinear relationships,and the proposed method performs well in the processing of censored data.

关 键 词：删失数据 部分线性可加模型 复合分位数回归 数据增广 

分 类 号：O212.1[理学—概率论与数理统计]