数学物理学报(英文版)

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

周勇; 吴国富; 李道纪   

  1. 中国科学院数学与系统科学研究院, 北京 100080
  • 收稿日期:2004-01-10 修回日期:2004-11-03 出版日期:2006-10-20 发布日期:2006-10-20
  • 通讯作者: 周勇
  • 基金资助:

    Zhou's research was partially supported by the NNSF of China (10471140, 10571169); Wu's research was partially supported by NNSF of China (0571170)

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

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摘要：

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 quantilefunction, kernel estimator, Bahadur representation

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

中图分类号: 

  • 62G05
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