左截断右删失数据分位差估计及其渐近性质

荀立, 周勇

数学学报 ›› 2017, Vol. 60 ›› Issue (3) : 451-464.

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数学学报 ›› 2017, Vol. 60 ›› Issue (3) : 451-464. DOI: 10.12386/A2017sxxb0037
论文

左截断右删失数据分位差估计及其渐近性质

    荀立1, 周勇2,3
作者信息 +

Estimators and Their Asymptotic Properties for Quantile Difference with Left Truncated and Right Censored Data

    Li XUN1, Yong ZHOU2,3
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文章历史 +

摘要

我们研究了左截断右删失数据分位差,基于左截断右删失数据乘积限构造了分位差的经验估计,同时克服经验估计的非光滑性,提出了分位数差的核光滑估计. 利用经验过程理论推导出这两个估计的渐近偏差和渐近方差,并且在左截断右删失数据下研究了这两个分位差的大样本性质,获得分位差估计的相合性和渐近正态性. 同时给出计算模拟以验证光滑分位差估计的表现,在均方损失的意义下模拟结果表明光滑估计比经验估计具有更好的性质.

Abstract

We investigate the asymptotic properties of the estimators of quantile difference based on left truncated and right censored data. The TJW product-limit estimator of the distribution function with the left truncated and right censored data is used to provide the empirical estimator of the quantile difference. Meanwhile, another smoothed kernel estimator for the quantile difference is established. Using the theory of empirical process, the expressions of the asymptotic bias and variance of the two estimators are derived. The large sample properties, such as consistency and asymptotic normality, for the estimators are obtained. A small simulation study shows that in the sense of mean squared loss, the smoothed estimator is more efficient than the non-smoothed estimator.

关键词

左截断右删失数据 / 分位差 / 相合性 / 渐近正态性 / 均方误差

Key words

left truncated and right censored data / quantile difference / consistency / asymptotic normality / mean squared error

引用本文

导出引用
荀立, 周勇. 左截断右删失数据分位差估计及其渐近性质. 数学学报, 2017, 60(3): 451-464 https://doi.org/10.12386/A2017sxxb0037
Li XUN, Yong ZHOU. Estimators and Their Asymptotic Properties for Quantile Difference with Left Truncated and Right Censored Data. Acta Mathematica Sinica, Chinese Series, 2017, 60(3): 451-464 https://doi.org/10.12386/A2017sxxb0037

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基金

国家自然科学基金重点资助项目(71331006)和国家自然科学基金资助项目(71271128);中科院重点实验室、国家数学与交叉科学中心,长江学者和教育部创新团队发展计划(IRT13077);上海财经大学创新团队支持计划资助

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