右删失长度偏差数据分位数差的非参数估计

刘玉涛, 潘婧, 周勇

数学学报 ›› 2020, Vol. 63 ›› Issue (2) : 105-122.

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数学学报 ›› 2020, Vol. 63 ›› Issue (2) : 105-122. DOI: 10.12386/A2020sxxb0009
论文

右删失长度偏差数据分位数差的非参数估计

    刘玉涛1, 潘婧2, 周勇3
作者信息 +

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

    Yu Tao LIU1, Jing PAN2, Yong ZHOU3
Author information +
文章历史 +

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.

Abstract

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

Key words

right-censored / length-biased data / quantile difference / empirical process

引用本文

导出引用
刘玉涛, 潘婧, 周勇. 右删失长度偏差数据分位数差的非参数估计. 数学学报, 2020, 63(2): 105-122 https://doi.org/10.12386/A2020sxxb0009
Yu Tao LIU, Jing PAN, Yong ZHOU. Nonparametric Estimation of the Quantile Differences for Right-censored and Length-biased Data. Acta Mathematica Sinica, Chinese Series, 2020, 63(2): 105-122 https://doi.org/10.12386/A2020sxxb0009

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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)

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