误差为线性过程时非参数回归模型变点的两步估计(英文)  

Two-step Change-point Estimation for Nonparametric Regression Model with Linear Process Errors

作　　者：赵文芝[1] 田铮[1] 夏志明[2] 

机构地区：[1]西北工业大学应用数学系,西安710072 [2]西北大学数学系,西安710069

出　　处：《工程数学学报》2009年第4期721-730,共10页Chinese Journal of Engineering Mathematics

基　　金：The National Natural Science Foundation of China (60375003);The Astronautics Basal Science Foundation of China (03I53059)

摘　　要：本文给出误差为线性过程时非参数回归模型变点两步估计。第一步,给出变点位置的初始估计,并且证明了该估计量的相合性;第二步,在变点初始估计值的基础上推导出变点位置的最终估计量并给出了该估计量的收敛速度。数值模拟以及尼罗河数据实例分析的结果说明方法的有效性。We consider the change point estimation problem in the nonparametric regression model with linear process errors. We propose a two-step estimator for the location of this change point. In the first step, an initial estimator of change point is obtained and the consistence of the change point is proved. In the second step, by comparing heights of function estimators on either side of a candidate value for the change point, the final change point estimator is proposed. It is shown that this estimator attains the rate Op（n^-1）. The method turns out to be effective after being tested on simulated examples and applied to the Nile river data.

关 键 词：非参数回归模型 变点 线性过程 弱相合性 收敛速度 

分 类 号：O212.7[理学—概率论与数理统计]