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高校应用数学学报
Applied Mathematics A Journal of Chinese Universities  2018, Vol. 33 Issue (2): 191-201    DOI:
    
The convergence of LS estimator for nonlinear regression models based on m-WOD errors
ZHU Yan-bei1;2, ZONG Rui-xue1;3, QIAO Xu-dong1, ZHAO Zhang-rui1, YANG Wen-zhi1
1. School of Mathematical Sciences, Anhui University, Hefei, 230601, China;
2. School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, 100081, China;
3. College of Mathematics and Information Science, Guangxi University, Nanning, 530004, China
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Abstract  Combining the conception of m dependent random variables with WOD random
variables, the conception of m-WOD random variables is given in this paper, which contains many
negative dependent random variables such as NA, m-NA, NSD, NOD, END, m-END and WOD. Based
on the m-WOD errors, the least squares (LS) estimator of nonlinear regression models is investigated
and some probability inequalities for the LS estimator are obtained. As an application, the complete
convergence and convergence in probability are presented under di?erent moment conditions, which
generalize the corresponding results.

Key words： nonlinear regression models      WOD random variables      least squares estimator      consistency     
Published: 26 July 2018
CLC:  O212.1  
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ZHU Yan-bei
ZONG Rui-xue
QIAO Xu-dong
ZHAO Zhang-rui
YANG Wen-zhi
Cite this article:

ZHU Yan-bei, ZONG Rui-xue, QIAO Xu-dong, ZHAO Zhang-rui, YANG Wen-zhi. The convergence of LS estimator for nonlinear regression models based on m-WOD errors. Applied Mathematics A Journal of Chinese Universities, 2018, 33(2): 191-201.

URL:

http://www.zjujournals.com/amjcua/     OR     http://www.zjujournals.com/amjcua/Y2018/V33/I2/191


m-WOD误差下非线性回归模型LS估计收敛性

结合m相依随机变量和WOD随机变量的概念, 给出m-WOD随机变量的概念,
它包含了NA随机变量, m-NA随机变量, NSD随机变量, NOD随机变量, END随机变
量, m-END随机变量, WOD随机变量等负相依随机变量. 基于误差为m-WOD随机变
量, 我们研究非线性回归模型参数最小二乘(LS)估计, 获得了参数LS估计的概率不等
式. 作为应用, 在不同的矩条件下, 获得LS估计的完全收敛速度和依概率收敛速度, 推
广了已有文献的结果.

关键词： 非线性回归模型,  WOD随机变量,  最小二乘估计,  相合性 
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