α混合样本下积分权回归估计的强相合性  

STRONG CONSISTENCY OF INTERGRAL WEIGHT REGRESSION ESTIMATOR FOR α-MIXING SAMPLES

作　　者：杨秀桃[1,2] 杨善朝 YANG Xiu-tao;YANG Shan-chao(Teaching and Research Department of Applied Mathematics,Faculty of Network Science,Haikou University of Economics,Haikou 571127,China;Department of Applied Statistics,College of Mathematics and Statistics,Guangxi Normal University,Guilin 541004,China)

机构地区：[1]海口经济学院网络学院应用数学教研室,海南海口571127 [2]广西师范大学数学与统计学院应用统计教研室,广西桂林541004

出　　处：《数学杂志》2019年第6期878-888,共11页Journal of Mathematics

基　　金：海南省自然科学基金资助(117173);国家自然科学基金资助(11461009)

摘　　要：本文在α混合样本下研究Gasser和Müller提出的一类积分权非参数核回归估计的大样本性质.利用α混合序列的概率指数不等式和矩不等式,在较弱的条件下获得了积分权回归函数估计的强相合性与一致强相合性,推广了独立样本下该回归函数估计的相合性结果.This paper is to study the large sample properties of a class of integral weight nonparametric kernel regression estimators proposed by Gasser and Müller underαmixing samples.By using the probability exponential inequality and the moment inequality ofαmixing sequences,the strong consistency and uniform strong consistency of the integral weight regression function estimator are obtained under weaker conditions,which extend the relevant conclusions of the regression function estimator under independent samples.

关 键 词：α混合样本 积分权回归估计 强相合性 一致强相合性 

分 类 号：O212.7[理学—概率论与数理统计] O211.4[理学—数学]