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bahadur representation OF THEKERNEL QUANTILE ESTIMATOR UNDER TRUNCATED AND CENSORED DATA

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Acta Mathematicae Applicatae Sinica 1999年第3期15卷 257-268页

作者：孙六全郑忠国 Institute of Applied Mathematics the Chinese Academy of Scienses Beijing China Department of Probability and Statistics Peking University Beijing China

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.

关键词： Kernel quantile density estimator bahadur representation left truncation and right censoring LIL asymptotic normality

Nonparametric Inference in a Simple Change-point Model

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Acta Mathematica Sinica,English Series 2008年第9期24卷 1483-1496页

作者： Zhan Feng Wang Yao Hua Wu and Lin Cheng Zhao Department of Statistics and Finance University of Science and Technology of China Hefei 230026 P. R. China

In this paper, we consider a change point model allowing at most one change, X($\tfrac{i}{n}$\tfrac{i}{n}) = f($\tfrac{i}{n}$\tfrac{i}{n}) + e($\tfrac{i}{n}$\tfrac{i}{n}), where f(t) = α + θ $I_{(t_0 ,1)} $I_{(t_0 ,1)} (t), 0 ≤ t ≤ 1, {e($\tfrac{1}{n}$\tfrac{1}{n}), ..., e($\tfrac{n}{n}$\tfrac{n}{n})} is a sequence of i.i.d. random variables distributed as e with 0 being the median of e. For this change point model, hypothesis test problem about the change-point t0 is studied and a test statistic is constructed. Furthermore, a nonparametric estimator of t0 is proposed and shown to be strongly consistent. Finally, we give an estimator of jump θ and obtain it’s asymptotic property. Performance of the proposed approach is investigated by extensive simulation studies.

关键词： sample median change point extreme distribution bahadur representation

A KERNEL-TYPE ESTIMATOR OF A QUANTILE FUNCTION UNDER RANDOMLY TRUNCATED DATA

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Acta Mathematica Scientia 2006年第4期26卷 585-594页

作者：周勇吴国富李道纪 Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100080China

A kernel-type estimator of the quantile function Q（p） = inf{t：F（t） ≥ p}, 0 ≤ p ≤ 1, is proposed based on the kernel smoother when the data are subjected to random truncation. The bahadur-type representations of the kernel smooth estimator are established, and from bahadur representations the authors can show that this estimator is strongly consistent, asymptotically normal, and weakly convergent.

关键词： Truncated data Product-limits quantile function kernel estimator bahadur representation

Some Limit Theorems for Kernel-Smooth Quantile Estimators

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Journal of Mathematical Research with Applications 1997年第4期 24-30页

作者： Zhou Yong (Inst. of Appl. Math., Academia Sinica, Beijing 100080)

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关键词： bahadur representation sample quantile empirical process and quantile process.