WOD随机变量序列加权和的矩完全收敛性  

Complete moment convergence of weighted sum of sequence of WOD random variables

作　　者：潘晓映 王美涵 施建华 张荣茂 PAN Xiaoying;WANG Meihan;SHI Jianhua;ZHANG Rongmao(School of Mathematics and Statistics,Minnan Normal University,Zhangzhou 363000,China;Fujian Key Laboratory of Granular Computing and Applications,Zhangzhou 363000,China;Fujian Key Laboratory of Data Science and Statistics,Zhangzhou 363000,China;Institute of Meteorological Big Data-Digital Fujian,Zhangzhou 363000,China)

机构地区：[1]闽南师范大学数学与统计学院,福建漳州363000 [2]福建省粒计算及其应用重点实验室,福建漳州363000 [3]福建省数据科学与统计重点实验室,福建漳州363000 [4]数字福建气象大数据研究所,福建漳州363000

出　　处：《纯粹数学与应用数学》2023年第2期250-269,共20页Pure and Applied Mathematics

基　　金：福建省自然科学基金(2020J01794,2021J01981,2021J01982);福建省社会科学基金(FJ2021C027).

摘　　要：WOD(widely orthant dependent)随机变量序列是一类非常宽泛的相依随机变量序列,应用WOD随机变量序列部分和的Menshov-Rademacher型不等式,结合五段截尾技术,研究得到了同分布WOD随机变量序列的Sung型加权和的最大值矩完全收敛性定理,推广和改进了已有的文献的一些最新结果.作为主要结果的一个应用,同时考虑了基于WOD误差的非参数回归模型中加权估计的完全相合性的结果,并且通过模拟验证了理论结果的有效性.The sequence of WOD(widely orthant dependent)random variables is a kind of very wide sequence of dependent random variables.Using the Menshov-Rademacher type inequality of the partial sum of WOD random variable sequences,combined with the five-stage truncation technique,the authors study a moment complete convergence theorem of Sung′s type weighted sums of identically distributed WOD random variable sequences.The results generalize and improve some of the corresponding results of the existing literature.As an application of the main results,we also considered the results of the complete consistency of the weighted estimates in the nonparametric regression model based on WOD errors,and verified the theoretical results through simulations.

关 键 词：WOD随机变量 加权和 矩完全收敛 非参数回归模型 

分 类 号：O178[理学—数学]