Acta mathematica scientia,Series B

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

Zhou Yong; Wu Guofu; Li Daoji   

  1. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China
  • Received:2004-01-10 Revised:2004-11-03 Online:2006-10-20 Published:2006-10-20
  • Contact: Zhou Yong

Abstract:

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.

Key words: Truncated data, Product-limits quantilefunction, kernel estimator, Bahadur representation

CLC Number: 

  • 62G05
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