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强混合样本下最近邻密度估计的渐近正态性
引用本文: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(中文版),2016,37(4):463-472.
作者姓名:秦永松  雷庆祝
作者单位:广西师范大学数学系, 广西 桂林\ 541004.,广西师范大学数学系, 广西 桂林\ 541004.
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.
摘    要:研究了α-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α-混合样本下概率密度的渐近置信区间.

关 键 词:$\alpha$-\!\!混合样本    最近邻密度估计    渐近正态性
收稿时间:2013/11/13 0:00:00
修稿时间:2015/6/13 0:00:00

Asymptotic Normality of the Nearest Neighbor Density Estimators under Strong Mixing Samples
QIN Yongsong and LEI Qingzhu.Asymptotic Normality of the Nearest Neighbor Density Estimators under Strong Mixing Samples[J].Chinese Annals of Mathematics,2016,37(4):463-472.
Authors:QIN Yongsong and LEI Qingzhu
Institution:Department of Mathematics, Guangxi Normal University, Guilin 541004, Guangxi, China. and Department of Mathematics, Guangxi Normal University, Guilin 541004, Guangxi, China.
Abstract: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.
Keywords:$\alpha$-Mixing sample  Nearest neighbor density estimator  Asymptotic normality
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