φ-混合样本下密度函数在有限点处的联合渐近分布  

The Joint Asymptotic Distribution of Probability Density Function in a Finite Number of Points Under φ-mixing Samples

作　　者：吴金蔚 WU Jinwei(College of Mathematics and Statistics,Xinyang Normal University,Xinyang 464000,China)

机构地区：[1]信阳师范学院数学与统计学院,河南信阳464000

出　　处：《信阳师范学院学报（自然科学版）》2021年第4期541-544,共4页Journal of Xinyang Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11901503);信阳师范学院青年骨干教师资助计划(2018GGJS-15)。

摘　　要：在φ-混合样本情形下,利用大小分块技术和矩不等式研究有限点处密度函数核估计的联合渐近分布,证明了渐近分布为多元正态分布.同时作为该结果的一个应用,还给出了任意两点处密度函数差的估计的渐近分布.The joint asymptotic distribution of kernel estimator of probability density function in a finite number of points is studied and proved under φ-mixing samples.By applying the blockwise technique and moment inequalities,it is shown that the joint asymptotic distribution is asymptotically multivariate normal distributed.As its application,the asymptotic distribution of the difference of density function between any two points is given.

关 键 词：φ-混合样本 密度函数 核估计 

分 类 号：O212.7[理学—概率论与数理统计]