长相依部分线性EV模型的小波估计的弱相合性  

Weak Consistency of Wavelet in Partly Linear Regression Errors-in-Variables Models

作　　者：刘香 胡宏昌 余新新 LIU Xiang;HU Hong-Chang;YU Xin-xin(Hubei Normal University,Huangshi 435002,China)

机构地区：[1]湖北师范大学数学与统计学院

出　　处：《数学的实践与认识》2018年第16期248-263,共16页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11471105)

摘　　要：在部分线性回归模型基础上,本文对自变量x进行了变形,使部分线性回归模型变为EV模型,yk=xkβ＋g（tk）＋εk,Xk=xk＋uk,k=1,2,…,n,自变量xk只能通过Xk=xk＋uk来观测,其中误差是非长相依的,并采用小波估计方法对结论进行证明.对水文地理学,经济学,时间序列分析和其他科学领域都有作用.This paper based on partially linear regression, changes the form of independent variables xk, transforms the partially linear regression modle into errors-in-variables modle yk=xkβ＋g（tk）＋εk,Xk=xk＋uk,k=1,2,…,n. The independent variables can＇t be observed directly, and there exist an independent observation errors uk between independent variables and observations. Then uses the wavelet method to prove the theorems. The results in this paper can be sued in many fields, such as hydrology, economics, time series analysis and other science.

关 键 词：长相依 部分线性EV模型 小波估计 弱相合性 

分 类 号：O212.1[理学—概率论与数理统计]