广西师范大学学报（自然科学版） ›› 2015, Vol. 33 ›› Issue (1): 80-85.doi: 10.16088/j.issn.1001-6600.2015.01.013

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KL分位数估计的Bahadur表示

郑丽霞1, 杨善朝2, 王章俊2   

  1. 1. 广西师范大学漓江学院,广西桂林541004;
    2. 广西师范大学数学与统计学院,广西桂林541004
  • 收稿日期:2014-09-29 出版日期:2015-03-15 发布日期:2018-09-17
  • 通讯作者: 杨善朝(1957-),男,广西玉林人,广西师范大学教授。E-mail:scyang@gxnu.edu.cn
  • 基金资助:
    国家自然科学基金资助项目(11461009)

The Bahadur Representation of KL Quantile Estimation

ZHENG Li-xia1, YANG Shan-chao2, WANG Zhang-jun2   

  1. 1. Lijiang College, Guangxi Normal University, Guilin Guangxi 541004, China;
    2. College of Mathematics and Statistics, Guangxi Normal University, Guilin Guangxi 541004, China
  • Received:2014-09-29 Online:2015-03-15 Published:2018-09-17

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摘要： Bahadur表示对于分位数估计的大样本性质的研究有着重要的作用,本文在独立样本的条件下,证明了KL分位数估计的Bahadur表示及其收敛速度op(k-1/2n),并通过Bahadur表示给出了其渐近正态性和置信区间估计。

关键词: KL分位数, Bahadur表示, 渐近正态性

Abstract: The Bahadur representation plays an important role in studying asymptotic properties of sample quantile estimation. In this paper, under the conditions of independent samples, the Bahadur of KL quantile estimation and its convergence rate op(k-1/2n) are derived. The asymptotic normality and the confidence interval estimation of the KL quantile estimation are also presented.

Key words: KL quantile estimation, Bahadur representation, asymptotic normality

中图分类号: 

  • O211.4
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[1] 杨善朝, 梁丹. φ混合样本下频率插值密度估计的强相合性[J]. 广西师范大学学报（自然科学版）, 2012, 30(3): 16-21.
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