[1]刘艳,吴群英.ND样本最近邻密度估计的一致强相合性[J].华侨大学学报(自然科学版),2012,33(5):590-594.[doi:10.11830/ISSN.1000-5013.2012.05.0590]
　LIU Yan,WU Qun-ying.Uniform Strong Consistency of Nearest Neighbor Estimator of Density Function for Negative Dependent Samples[J].Journal of Huaqiao University(Natural Science),2012,33(5):590-594.[doi:10.11830/ISSN.1000-5013.2012.05.0590]
点击复制

ND样本最近邻密度估计的一致强相合性()
分享到：

《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第33卷
期数:
2012年第5期
页码:
590-594
栏目:
出版日期:
2012-09-20

文章信息/Info

Title:
Uniform Strong Consistency of Nearest Neighbor Estimator of Density Function for Negative Dependent Samples
文章编号:
1000-5013(2012)05-0590-05
作者:
刘艳;  吴群英
桂林理工大学 理学院, 广西 桂林 541004
Author(s):
LIU Yan;  WU Qun-ying
College of Science, Guilin University of Technology, Guilin 541004, China
关键词:
负相依序列;  最近邻密度估计;  一致强相合性;  Bernstein不等式
Keywords:
negative dependent sequence;  nearest neighbor density estimator;  Bernstein inequality
分类号:
O212.7
DOI:
10.11830/ISSN.1000-5013.2012.05.0590
文献标志码:
A
摘要:
设X1,X2,…,Xn是同分布的负相依(ND)样本,具有共同的密度函数f(x),利用相应的Bernstein不等式,将负相关(NA)样本最近邻密度估计的一致强相合性推广到ND样本,得到其最近邻密度估计的一致强相合性.
Abstract:
Suppose that X1,X2,…,Xn are negative dependent(ND)samples, with a common density function f(x). By the use of the corresponding Bernstein inequality, the uniform strong consistency of nearest neighbor estimator of density function for negatively associated(NA)samples is extended to ND samples, and the latter uniform strong consistency of nearest neighbor estimator of density function is obtained.

参考文献/References:

[1] LOFTSGARDEN D O,QUENSBERRY C D.A Nonparametric estimator of a multivariate density function[J].Ann Statist,1965,36(3):1049-1051.
[2] WAGNER T J.Strong consistency of a nonparametic estimate of a density function[J].IEEE Trans Systems Man Cybenet,1973(3):289-290.
[3] CHENG Xi-ru.Convergence rates for nearest neighbor density estimator[J].Sci China Ser A,1980(12):1419-1428.
[4] YANG Shan-chao.Consistency of nearest neighbor density function for pairwise NA sequence[J].Acta Math Application,2003,26(3):385-395.
[5] BOZORGNIA A,PATTERSON R F,TAYLOR R L.Limit theorems for ND r.v.’s[R].Athens:University of Georgia,1993.
[6] WU Qun-ying,JIANG Yuan-ying.The strong consistency of estimator in linear model for negatively dependent random samples[J].Communications in Statistics-Theory and Methods,2011,40(3):467-491.
[7] 杨善朝.NA样本最近邻密度估计的相合性[J].应用数报,2003,26(3):385-408.

备注/Memo

备注/Memo:
收稿日期: 2012-01-07
通信作者: 吴群英(1961-),女,教授,主要从事概率统计的研究.E-mail:wqy666@glite.edu.cn.
基金项目: 国家自然科学基金资助项目(11061012); 广西自然科学基金资助项目(2011GXNSFA018147); 广西研究生教育创新计划项目(2011105960202M32)
更新日期/Last Update: 2012-09-20