噪声为单位根过程的非参数函数变点的小波检测  

Wavelet detection of jumping points in a nonparametric function with the unit-root noise

作　　者：齐培艳[1,2] 田铮[1,3] 段西发[1,2] 李晓燕[1,3] 陈占涛[1,3] 

机构地区：[1]西北工业大学应用数学系,陕西西安710072 [2]太原科技大学数学系,山西太原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：《控制理论与应用》2009年第1期57-61,共5页Control Theory & Applications

基　　金：国家自然科学基金资助项目(60375003);国家航空基金资助项目(03I53059);西北工业大学科技创新基金资助项目(2007KJ01033)

摘　　要：利用小波方法和极限定理对噪声为单位根过程的非参数函数的跳跃点进行检测.首先,利用极限定理得到噪声的小波系数的极限分布.然后构造检验统计量,在原假设成立的条件下得到任意尺度上检验的临界值,证明了检验的一致性,并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.最后利用模拟研究与实例分析说明了方法的有效性和实用性,并与"UNI"方法以及"GOF"方法作比较,说明对于噪声为单位根过程的非参数函数变点的检测问题,本文所提的方法更加有效.We combine the wavelet method and the limit-theorem to test the presence of jumping-points in a nonparametric function which is observed with unit-root noise. First, the limit distribution of the wavelet coefficients of the noise is derived using the limit-theorem, and then, the statistic of detection is determined. When the null hypothesis holds, we obtain the critical values at any scale, prove the consistency of wavelet detection and give the threshold of wavelet coefficients. When the alternative hypothesis holds, the consistent estimation of the numbers and locations of jumping points are given and the rate of convergence is obtained. Simulation study and real data analysis support our method. Finally, we compare our method with the ＂UNI＂ -method and the ＂GOF＂ -method. Asymptotic results show that our method is more powerful in detecting the jumping points of nonparametric function with Unit-root noise.

关 键 词：变点 单位根过程 小波变换 收敛速度 

分 类 号：O213.1[理学—概率论与数理统计]