误差为单位根过程的非参数回归模型均值变点的检测  

Detecting Change-points in Mean of Nonparametric Regression Models with Unit-root Errors

作　　者：齐培艳[1,2] 田铮[1,3] 段西发[1,2] 

机构地区：[1]西北工业大学应用数学系,西安710072 [2]太原科技大学数学系,太原030024 [3]中国科学院遥感应用研究所遥感科学国家重点实验室,北京100101

出　　处：《工程数学学报》2010年第4期584-592,共9页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(60972150;10926197);西北工业大学科技创新基金(2007KJ01033)~~

摘　　要：基于多分辨分析的小波分析通过检测小波系数的绝对值来检测数据中的变点。本文利用小波方法和极限定理对噪声为单位根过程的非参数回归模型均值变点进行检测。在原假设成立的条件下得到任意尺度上检验的临界值,证明检验的一致性,并且给出小波系数的阈值。在备择假设成立的条件下,给出变点个数、变点位置的相合估计与收敛速度。最后利用模拟研究说明了方法的有效性和实用性。Based on the theory of multi-resolution analysis, the change-points in data can be detected by checking the absolute value of wavelet coeffcients. In this paper, we combine wavelet methods and the extreme value theory to establish an approach to test the presence of an arbitrary number of discontinuities for an unknown function, based on date observed with unit-root noise. If the null hypothesis holds, we obtain critical values at any scale and prove the consistency of wavelet detection. If the alternative hypothesis holds, we show that the estimation of the numbers and location of change points are consistent. Simulation study supports our method.

关 键 词：变点 单位根过程 小波变换 收敛速度 

分 类 号：O212.1[理学—概率论与数理统计]