| 随机设计下非参数回归模型变点的小波检测与估计 |
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| 引用本文： | 赵文芝,田铮,夏志明. 随机设计下非参数回归模型变点的小波检测与估计[J]. 数学研究及应用, 2009, 29(2): 247-256 |
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| 作者姓名： | 赵文芝 田铮 夏志明 |
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| 作者单位： | 西北工业大学应用数学系, 陕西 西安 710072;西北工业大学应用数学系, 陕西 西安 710072;西北大学数学系, 陕西 西安 710069 |
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| 基金项目： | 国家自然科学基金(No.60375003);能航空基础科学基金项目 (No.03I53059). |
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| 摘 要： | A wavelet method of detection and estimation of change points in nonparametric regression models under random design is proposed. The confidence bound of our test is derived by using the test statistics based on empirical wavelet coefficients as obtained by wavelet transformation of the data which is observed with noise. Moreover, the consistence of the test is proved while the rate of convergence is given. The method turns out to be effective after being tested on simulated examples and applied to IBM stock market data.
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| 关 键 词： | 随机设计 非参数回归模型 变点 小波 检测 估计 |
| 收稿时间： | 2007-06-22 |
| 修稿时间： | 2007-11-22 |
Wavelet Detection and Estimation of Change Points in Nonparametric Regression Models under Random Design |
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| ZHAO Wen Zhi,TIAN Zheng and XIA Zhi Ming. Wavelet Detection and Estimation of Change Points in Nonparametric Regression Models under Random Design[J]. Journal of Mathematical Research with Applications, 2009, 29(2): 247-256 |
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| Authors: | ZHAO Wen Zhi TIAN Zheng XIA Zhi Ming |
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| Affiliation: | Department of Applied Mathematics, Northwestern Polytechnical University, Shaanxi 710072, China;Department of Applied Mathematics, Northwestern Polytechnical University, Shaanxi 710072, China;Department of Mathematics, Northwest University, Shaanxi 710069, China |
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| Abstract: | A wavelet method of detection and estimation of change points in nonparametric regression models under random design is proposed. The confidence bound of our test is derived by using the test statistics based on empirical wavelet coefficients as obtained by wavelet transformation of the data which is observed with noise. Moreover, the consistence of the test is proved while the rate of convergence is given. The method turns out to be effective after being tested on simulated examples and applied to IBM stock market data. |
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| Keywords: | random design nonparametric regression model change point wavelet transformation consistent test rate of convergence. |
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