秦永松,雷庆祝.强混合样本下最近邻密度估计的渐近正态性[J].数学年刊A辑,2016,37(4):463~472
强混合样本下最近邻密度估计的渐近正态性
Asymptotic Normality of the Nearest Neighbor Density Estimators under Strong Mixing Samples
Received: November 13, 2013  Revised: June 13, 2015
DOI:
中文关键词:  $\alpha$-\!\!混合样本, 最近邻密度估计, 渐近正态性
英文关键词:$\alpha$-Mixing sample, Nearest neighbor density estimator, Asymptotic normality
基金项目:本文受到国家自然科学基金(No.11671102, No.11271088, No.11361011) 和广西省自然科学基金(No.2013GXNSF-AA019004, No.2013GXNSFAA019007)的资助.
Author NameAffiliation
QIN Yongsong Department of Mathematics, Guangxi Normal University, Guilin 541004, Guangxi, China. 
LEI Qingzhu Department of Mathematics, Guangxi Normal University, Guilin 541004, Guangxi, China. 
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中文摘要:
      研究了 $\alpha$-\!\!混合样本下最近邻密度估计的渐近性质, 证明了估计的渐近正态性并且给出了其渐近方差的显式表达式, 由此构造了 $\alpha$-\!\!混合样本下概率密度的渐近置信区间.
英文摘要:
      In this paper, the asymptotic normality of a nearest neighbor density estimator under an $\alpha$-mixing sample is studied. The authors obtain the asymptotic normality of the estimator with an explicit form of the asymptotic variance, which is used to construct the asymptotic confidence interval for a probability density function under an $\alpha$-mixing sample.
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