基于m-WOD序列非参数回归模型线性加权估计的完全收敛性  

Complete convergence for the linear weighted estimator of nonparametric regression model based on m-WOD sequence

作　　者：苏欣 王彬 SU Xin;WANG Bin(School of Mathematics,Boda College of Jilin Normal University,Siping 136000,China;Basic Department,Dalian University of Science and Technology,Dalian 116000,China)

机构地区：[1]吉林师范大学博达学院数学学院,吉林四平136000 [2]大连科技学院基础部,辽宁大连116000

出　　处：《白城师范学院学报》2024年第5期22-28,共7页Journal of Baicheng Normal University

摘　　要：利用m-WOD序列的性质和概率不等式,研究了基于m-WOD序列的非参数回归模型线性加权估计的完全收敛性并得到了其收敛速度.首先,给出了研究需要用到的预备知识.然后,证明了m-WOD序列的非参数回归模型线性加权估计的完全收敛性及其收敛速度.最后,以最近邻估计为例,验证了相应的完全收敛性及其收敛速度的正确性.This paper investigates the complete convergence and convergence rate of the linear weighted estimates of nonparametric regression model based on m-WOD sequences.First,the preliminary knowledge needed for the study is given.And then,the paper mainly proves the complete convergence and convergence rate of the linear weighted estimation of nonparametric regression model for m-WOD sequences.At last,taking the nearest neighbor estimation as an example,the corresponding complete convergence and convergence speed are verified.

关 键 词：m-WOD序列 非参数回归模型 线性加权估计 完全收敛性 

分 类 号：O212[理学—概率论与数理统计]