删失数据平滑非参数分位估计的Bahadur表示

刘焕彬;朱玉阶

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

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

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

    Liu Huanbin(1);Zhu Yujie(2)
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摘要

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.

Abstract

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.

关键词

右删失 / 平滑非参数分位估计 / Bahadur表示

Key words

Right-censoring / smooth nonparametric quantile estimator / Bahadur representation

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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. 系统科学与数学, 1996, 16(3): 260-269. https://doi.org/10.12341/jssms09200
Liu Huanbin , Zhu Yujie. THE BAHADUR REPRESENTAION OF A SMOOTH NONPARAMETRIC QUANTILE ESTIMATOR ON CENSORED DATA. Journal of Systems Science and Mathematical Sciences, 1996, 16(3): 260-269 https://doi.org/10.12341/jssms09200
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