右删失长度偏差数据分位数差的非参数估计  

Nonparametric Estimation of the Quantile Differences for Right-censored and Length-biased Data

作　　者：刘玉涛[1] 潘婧 周勇[3] Yu Tao LIU;Jing PAN;Yong ZHOU(School of Statistics and Mathematics,Central University of Finance and Economics,Beijing 100081,P.R.China;Research Institute of Electronic Payment,China Unionpay,Shanghai 201201,P.R.China;Key Laboratory of Advanced Theory and Application in Statistics and Data Science,Ministry of Education Institute of Statistics and Interdisciplinary Sciences and School of Statistics,Faculty of Economics and Management,East China Normal University,Shanghai 200241,P.R.China)

机构地区：[1]中央财经大学统计与数学学院,北京100081 [2]中国银联股份有限公司电子商务与电子支付国家工程实验室,上海201201 [3]统计与数据科学前沿理论及应用教育部重点实验室上海华东师范大学统计交叉科学研究院和统计学院,上海200241

出　　处：《数学学报（中文版）》2020年第2期105-122,共18页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学重大研究计划重点项目(91546202);国家自然科学基金委重点项目(71331006);国家自然科学基金(11401603);中央高校基本科研业务经费(QL18009);中央财经大学学科建设经费(CUFESAM201811)。

摘　　要：利用长度偏差数据所特有的辅助信息,对带右删失的长度偏差数据的分位数差提出了一种新的非参数估计.该方法提高了估计的有效性,所得的估计量形式简洁,便于计算.同时,本文用经验过程理论建立了该分位数差估计的相合性及渐近正态性,并给出方差估计的重抽样方法.本文还通过数值模拟考察了该估计量在有限样本下的表现,并将其应用到一个关于老年痴呆的实际数据中.We propose a novel nonparametric estimator of the quantile difference based on the length-biased data subject to potential right censoring.In order to improve efficiency,the new estimator incorporates the auxiliary information inherent in the prevalent sampling design.And it has a simple expression,which is easy to compute.Moreover,the consistency and asymptotic normality of this quantile difference estimator are established using the empirical process theory and the asymptotic variance can be obtained consistently via a resampling method.We also demonstrate that the proposed estimator exhibits satisfactory performance with finite sample size through the Monte-Carlo studies and an analysis of a real data example about the Alzheimer’s disease.

关 键 词：右删失 长度偏差数据 分位数差 经验过程 

分 类 号：O212[理学—概率论与数理统计] O212.1[理学—数学]