噪声为厚尾过程的非参数函数变点的小波估计  

Wavelet Estimation of Change-points in a Nonparametric Regression Function with Heavy-tailed Noise

作　　者：李晓燕[1] 田铮[1,2] 齐培艳[1] 赵文芝[1] 

机构地区：[1]西北工业大学应用数学系,西安710072 [2]西北工业大学计算机科学技术系,西安710072

出　　处：《工程数学学报》2010年第6期986-994,共9页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(60972150;10926197)~~

摘　　要：本文给出了随机设计下非参数回归模型中噪声为无穷方差过程的小波检测和估计方法。利用基于经验小波系数的检验统计量,在原假设成立的条件下,推导出任意尺度上检验的临界值,证明了检验的一致性;在备择假设成立的条件下,得到变点个数、变点位置的相合估计与收敛速度。数值模拟以及IBM股票数据实例分析的结果均表明方法是有效的。A wavelet method is proposed to detect and estimate change points in nonparametric regression models under random design,whose noise is a heavy tailed infinite-varianced process.If the null hypothesis holds,we obtain critical values at any scale and prove the consistency of the test by using the test statistics based on empirical wavelet coeffcients.If the alternative hypothesis holds,we show that the estimation of the numbers and location of change points are consistent.Numerical simulation results as well as the IBM stock data analysis indicate that the proposed method is effective.

关 键 词：随机设计 非参数回归模型 无穷方差过程 变点 小波估计 

分 类 号：O212.1[理学—概率论与数理统计]