半参数回归模型小波估计的稳定地依分布收敛性——误差为鞅差序列情形  

Stably Convergence in Distribution About Wavelet Estimation in Semiparametric Regression Model——The Martingale Difference Error Sequence Case

作　　者：胡宏昌[1] 孙海燕[1] 

机构地区：[1]武汉大学测绘学院

出　　处：《武汉大学学报（理学版）》2003年第5期571-574,共4页Journal of Wuhan University:Natural Science Edition

基　　金：国家自然科学基金资助项目(40274005);湖北省教育厅重大项目(2001Z06003)

摘　　要：考虑半参数回归模型yi=xiβ+g(ti)+εi,1≤i≤n,其中β∈R为未知参数,g(t)为[0,1]上的未知Borel函数,xi为R上的随机设计,随机误差序列{εi,1≤i≤n}为鞅差序列,{ti}为[0,1]上的常数序列.本文用小波的方法得到β及g(t)的估计β∧、g∧(t),并研究了n(β∧-β)稳定地依分布收敛于其准分布函数G.Consider the semiparameter regression modely_i=x_iβ+g(t_i)+ε_i,1≤i≤n where β is a unknown parameter, g(t) is an unknown Borel function on \, x_i is a random design, random error sequences {ε_i,1≤i≤n} is martingale difference sequences, {t_i} is constant sequence on\. In the paper, the estimators of β & g(t) are established by wavelet method, and stably convergence to quasi-distribution function G in distribution about n(β∧-β) is studied.

关 键 词：半参数回归模型 小波估计 稳定地依分布收敛性 准分布函数 鞅差序列 随机误差序列 

分 类 号：O212.1[理学—概率论与数理统计]