广西师范大学学报（自然科学版） ›› 2012, Vol. 30 ›› Issue (3): 16-21.

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φ混合样本下频率插值密度估计的强相合性

杨善朝, 梁丹   

  1. 广西师范大学数学科学学院,广西桂林541004
  • 收稿日期:2012-05-24 出版日期:2012-09-20 发布日期:2018-12-04
  • 通讯作者: 杨善朝(1957—),男,广西兴业人,广西师范大学教授。E-mail:scyang@mailbox.gxnu.edu.cn
  • 作者简介:杨善朝,男,汉族,1957年10月生,广西兴业县人,广西师范大学数学学科概率统计专业教授、享受国务院政府特殊津贴专家、广西优秀专家,广西十百千人才工程第二层次人选。
  • 基金资助:
    国家自然科学基金资助项目(11061007);广西自然科学基金资助项目(2011GXNSFA018133)

Strong Consistency of Frequency Polygon Density Estimator for φ Mixing Sequence

YANG Shan-chao, LIANG Dan   

  1. College of Mathematical Sciences,Guangxi Normal University,Guilin Guangxi 541004,China
  • Received:2012-05-24 Online:2012-09-20 Published:2018-12-04

摘要： Scott 1985年提出频率插值密度估计,并在独立样本条件下证明其均方误差收敛速度快于直方图估计,且达到与密度核估计一样的速度,所以它是一种较好的密度估计。Carbon等1997年在α混合样本下证明频率插值密度估计的强相合性及其收敛速度,Nadia和Sophie2010年将其结果推广到多元情形。本文则是将这些研究推广到φ混合样本情形,证明频率插值密度估计的强相合性,获得较好的收敛速度,并减弱了结论的条件。

关键词: 频率插值密度估计, φ混合样本, 强相合性

Abstract: Scott (1985) proposed a frequency polygon density estimation,and proved that it dominated the histogram with respect to the criterionof integrated mean squared error and had the same rate of convergence to zero of the integrated mean squared error as non-negative kernel estimator for independent samples.For α mixing sequence,Carbon et al (1997) showed the uniformly strong consistency of the frequency polygons estimate and the convergence rate.Nadia and Sophie (2010) extended these results to the multivariate case.This paper extends the research to the case of the φ mixing samples,and proves theuniformly strong consistency of the frequency polygons estimate,which getsbetter convergent rate and weakens the conditions used by Carbon et al (1997) and Nadia and Sophie (2010).

Key words: frequency polygon density estimate, φ mixing sequence, strong consistency

中图分类号: 

  • O211.4
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