左截断右删失数据下分位数差的估计

吉林大学学报(理学版) ›› 2018, Vol. 56 ›› Issue (5): 1105-1112.

左截断右删失数据下分位数差的估计

荀立, 崔世崇, 朵兰

长春工业大学数学与统计学院, 长春 130012

收稿日期:2017-10-10 出版日期:2018-09-26 发布日期:2018-11-22
通讯作者: 荀立 E-mail:xunli@ccut.edu.cn

Estimator of Quantile Difference with LeftTruncated and RightCensored Data#br#

XUN Li, CUI Shichong, DUO Lan

School of Mathematics and Statistics, Changchun University of Technology, Changchun 130012, China

Received:2017-10-10 Online:2018-09-26 Published:2018-11-22

摘要/Abstract

摘要： 首先, 利用核光滑方法研究左截断右删失数据下总体分位数差的估计, 得到了左截断右删失数据下分位数差的光滑估计及估计量的大样本性质. 其次, 在均方误差意义下, 证明了光滑分位数差估计比左截断右删失数据下乘积限分位函数的差有更高的估计效率. 最后数值模拟分析高斯核函数下选择不同窗宽对改善乘积限分位数差估计效率的影响.

关键词: 左截断右删失数据, 光滑分位函数, 乘积限分位函数, 分位数差

Abstract: Firstly, by using the kernel smooth method, we studied the estimation of the total quantile difference with lefttruncated and rightcensored (LTRC) data, and obtained the large sample properties of the smoothed estimators of quantile difference with LTRC data. Secondly, in the sense of mean square error, we proved the estimation efficiency of the smooth quantile difference was higher than that of the product limit quantile difference with LTRC data. Finally, we analyzed the effect of various bandwidths with Gaussian kernel function on the improved estimation efficiency of product limit quantile difference through numerical simulations.

Key words: lefttruncated and rightcensored (LTRC) data, smooth quantile function, product limit quantile function, quantile difference

中图分类号:

O212.7

荀立, 崔世崇, 朵兰. 左截断右删失数据下分位数差的估计[J]. 吉林大学学报(理学版), 2018, 56(5): 1105-1112.

XUN Li, CUI Shichong, DUO Lan. Estimator of Quantile Difference with LeftTruncated and RightCensored Data#br#[J]. Journal of Jilin University Science Edition, 2018, 56(5): 1105-1112.