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删失指标随机缺失下回归函数的复合分位数回归估计 被引量：2

Composite Quantile Regression Estimators of Regression Function with Censoring Indicators Missing at Random
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摘要 在非参数回归模型中,传统的Nadaraya-Watson核估计和局部多项式估计常常因为误差为重尾情况而变得不稳健,Kai等人(2010)提出的复合分位数回归方法能弥补这一缺陷.文章在删失指标随机缺失的情况下,研究了误差具有异方差结构的非参数删失回归模型,利用局部多项式方法构造了回归函数的复合分位数回归估计,并得到了该估计的渐近正态性结果,把Kai等人(2010)的结果推广到删失指标随机缺失的右删失数据下.最后通过模拟发现,尤其是当误差为重尾分布时,该估计方法比Wang和Zheng (2014)提出的核估计方法更好. In the nonparametric regression model, the Nadaraya-Watson kernel estimation and local polynomial estimation are not robust when the error is heavy tailed. The composite quantile regression method proposed by Kai, et al. (2010) can overcome the shortcoming of robustness. In this paper, we consider the nonparametric regression model with heteroscedastic error when the data are right-censored and the censoring indicators are missing at random, construct the composite quantile regression estimators of regression function based on the local polynomial method, and establish the asymptotic normality of these estimators, which extends the results of the Kai, et al. (2010) to right-censored data with the censoring indicators missing at random. The simulation studies show that our estimators perform better than the kernel estimation proposed by Wang and Zheng (2014), especially when the error is the heavy tail distribution.
作者 王江峰 范国良 温利民 WANG Jiangfeng;FAN Guoliang;WEN Limin(School of Statistics and Mathematics,Zhejiang Gongshang University,Hangzhou 310018;School of Economics and Management,Shanghai Maritime University,Shanghai 201306;Institute of Statistics and Big Data,Renmin University of China,Beijing 100872;School of Mathematics and Information Science,Jiangxi Normal University,Nanchang 330022)
机构地区 浙江工商大学统计与数学学院 上海海事大学经济管理学院 中国人民大学统计与大数据研究院 江西师范大学数学与信息科学学院
出处 《系统科学与数学》 CSCD 北大核心 2018年第11期1347-1362,共16页 Journal of Systems Science and Mathematical Sciences
基金 国家社科基金(16BTJ029) 国家自然科学基金(71761019) 教育部人文社科基金(15YJC910006) 国家统计局重点项目(2016LZ05) 浙江省自然科学基金(LY18A010007) 浙江省一流学科A类(浙江工商大学统计学)资助(OOOOJYN6516003G-19) 中国博士后科学基金项目资助(2018T110174 2017M611083) 江西省自然科学基金(20171ACB21022)资助课题
关键词 右删失数据 删失指标 随机缺失 非参数回归 复合分位数回归 渐近正态性 Rigth-censored data censoring indicator missing at random nonpara- metric regression composite quantile regression asymptotic normality.
分类号 O212.1 [理学—概率论与数理统计]
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系统科学与数学
2018年 第11期

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