| 无穷方差厚尾过程中非参数函数的小波估计 |
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| 引用本文： | 段西发,田铮,齐培艳.无穷方差厚尾过程中非参数函数的小波估计[J].数理统计与管理,2010,29(2). |
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| 作者姓名： | 段西发 田铮 齐培艳 |
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| 作者单位： | 1. 太原科技大学数学系,山西,太原,030024;西北工业大学应用数学系,陕西,西安,710072
2. 西北工业大学应用数学系,陕西,西安,710072 |
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| 基金项目： | 国家自然科学基金(60375003); 国家航空基金项目(03153059); 西北工业大学创新基金(2007KJ01033) |
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| 摘 要： | 研究无穷方差厚尾过程中含有变点的非参数函数的估计问题。通过小波方法给出变点位置的估计值并得到其收敛速度。在已知变点估计值的基础上,将截尾方法与小波压缩方法相结合得到非参数函数的估计值。模拟研究结果说明对于无穷方差厚尾过程中的函数估计问题小波方法是有效的。
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| 关 键 词： | 无穷方差厚尾过程 非参数函数 变点 收敛速度 |
Wavelet Estimation of Nonparametric Function in Heavy-tailed Process with Infinite Variance |
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| DUAN Xi-fa,TIAN Zheng,QI Pei-yan.Wavelet Estimation of Nonparametric Function in Heavy-tailed Process with Infinite Variance[J].Application of Statistics and Management,2010,29(2). |
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| Authors: | DUAN Xi-fa TIAN Zheng QI Pei-yan |
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| Institution: | DUAN Xi-fa~(1,2) TIAN Zheng~2 QI Pei-yan~(1,2) (1.Taiyuan University of Science , Technology,Department of Mathematics,Shanxi Taiyuan 030024,China,2.Department of Applied mathematics,Northwestern Polytechnical University,Shaanxi Xi\'an,710072,China) |
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| Abstract: | In this paper,we study the estimation of nonparametric function in heavy-tailed process with infinite variance.First,we propose a sharp change point estimator by wavelets and has the convergence rate.Next,we estimate the nonparametric function based on the change point estimator by truncating tail and wavelet shrinkage.Simulation study show that our method is available for estimation of nonparametric function in heavy-tailed process with infinite variance. |
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| Keywords: | heavy-tailed process with infinite variance nonparametric function change-point the rate of convergence |
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