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BAHADUR REPRESENTATION OF THEKERNEL QUANTILE ESTIMATOR UNDER TRUNCATED AND CENSORED DATA
作者姓名:孙六全  郑忠国
作者单位:SUN LIUQUAN (Institute of Applied Mathematics,the Chinese Academy of Scienses,Beijing 100080,China)ZHENG ZHONGGUO (Department of Probability and Statistics,Peking University,Beijing 100871,China)
摘    要:1.IntroductionTheestimationofpopulationquaillesisofgrestillterestwhenone.isnotpreparedtoassumeaparametricformfortheunderlyingdistribution.Inaddition,quaillesoftenariseasthensturalthingtoestimatewhentheunderlyingdistributionisskewed.LetXIIXZ,')Xubei...

收稿时间:4 November 1996

Bahadur representation of the kernel quantile estimator under truncated and censored data
Sun Liuquan,Zheng Zhongguo.BAHADUR REPRESENTATION OF THEKERNEL QUANTILE ESTIMATOR UNDER TRUNCATED AND CENSORED DATA[J].Acta Mathematicae Applicatae Sinica,1999,15(3):257-268.
Authors:Sun Liuquan  Zheng Zhongguo
Institution:(1) Institute of Applied Mathematics, the Chinese Academy of Scienses, 100080 Beijing, China;(2) Department of Probability and Statistics, Peking University, 100871 Beijing, China
Abstract:In this article the authors establish the Bahadur type representations for the kernel quantileestimator and the kernel estimator of the derivatives of the quantile function on the basis of lefttruncated and right censored data. Under suitable conditions, with probability one, the exactconvergence rate of the remainder term in the representations is obtained. As a by-product, theLIL, the asymptotic normality for those kernel estimators are derived.
Keywords:Kernel quantile density estimator  Bahadur representation  left truncation and right censoring  LIL  asymptotic normality
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