删失数据平滑非参数分位估计的Bahadur表示

doi:10.12341/jssms09200

系统科学与数学 ›› 1996, Vol. 16 ›› Issue (3): 260-269.DOI: 10.12341/jssms09200

删失数据平滑非参数分位估计的Bahadur表示

刘焕彬(1);朱玉阶(2)

(1)湖北黄冈师范专科学校数学系;(2)浙江湖州师范专科学校数学系

收稿日期:1900-01-01 修回日期:1900-01-01 出版日期:1996-07-25 发布日期:1996-07-25

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刘焕彬;朱玉阶. 删失数据平滑非参数分位估计的Bahadur表示[J]. 系统科学与数学, 1996, 16(3): 260-269.

Liu Huanbin;Zhu Yujie. THE BAHADUR REPRESENTAION OF A SMOOTH NONPARAMETRIC QUANTILE ESTIMATOR ON CENSORED DATA[J]. Journal of Systems Science and Mathematical Sciences, 1996, 16(3): 260-269.

THE BAHADUR REPRESENTAION OF A SMOOTH NONPARAMETRIC QUANTILE ESTIMATOR ON CENSORED DATA

Liu Huanbin(1);Zhu Yujie(2)

(1)Department of Mathematics,Huanggang Teachers' Collage,Hubei 436100;(2)Department of Mathematics,Huzhou Teachers' College,Zhejiang 313000

Received:1900-01-01 Revised:1900-01-01 Online:1996-07-25 Published:1996-07-25

本文讨论了在随机右删失情况下一种平滑非参数分位估计x_n(p)(x_n(p)是F_n(x)=\int^x_{-\infty}\int_{-infty}^{\infty}h_n^{-1}K((t-y)/h_n)d\hat{F}_n(y)dt-p的解)．在一定的条件下获得了x_n(p)的Bahadur表示，作为推论获得了x_n(p)的渐近正态分布和重对数律．

关键词： 右删失, 平滑非参数分位估计, Bahadur表示

On the basis of randomly right-censored data,a smooth nonparametric quantile estimator is studied.The estimator is defined to be the solution xn(p) of Fn(x)=p,where Fn(x)=Under some conditions,we obtain the Bahadur representation of xn(p).Using this result,we derive the asymptotic normal distribution and the iterated logarithm law.

Key words: Right-censoring, smooth nonparametric quantile estimator, Bahadur representation

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