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中文摘要：
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。
英文摘要：
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.
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