| BOOTSTRAP WAVELET IN THE NONPARAMETRIC REGRESSION MODEL WITH WEAKLY DEPENDENT PROCESSES |
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| 作者姓名： | 林路 张润楚 |
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| 作者单位： | [1]SchoolofMathematicsandSystemSciences,ShandongUniversity,Jinan250100,China [2]SchoolofMathematicalSciences,NankaiUniversity,Tianjin300071,China |
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| 摘 要： | This paper introduces a method of bootstrap wavelet estimation in a nonparametric regression model with weakly dependent processes for both fixed and random designs. The asymptotic bounds for the bias and variance of the bootstrap wavelet estimators are given in the fixed design model. The conditional normality for a modified version of the bootstrap wavelet estimators is obtained in the fixed model. The consistency for the bootstrap wavelet estimator is also proved in the random design model. These results show that the bootstrap wavelet method is valid for the model with weakly dependent processes.
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| 关 键 词： | 自助法 小波分析 非参数衰退模型 弱相依性 |
| 收稿时间： | 6 July 2001 |
BOOTSTRAP WAVELET IN THE NONPARAMETRIC REGRESSION MODEL WITH WEAKLY DEPENDENT PROCESSES |
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| Lin Lu Zhang Runchu
.School of Mathematics and System Sciences,Shandong University,Jinan ,China .School of Mathematical Sciences,Nankai University,Tianjin ,China.BOOTSTRAP WAVELET IN THE NONPARAMETRIC REGRESSION MODEL WITH WEAKLY DEPENDENT PROCESSES[J].Acta Mathematica Scientia,2004,24(1):61-70. |
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| Authors: | Lin Lu Zhang Runchu
School of Mathematics and System Sciences Shandong University Jinan China School of Mathematical Sciences Nankai University Tianjin China |
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| Institution: | Lin Lu Zhang Runchu
2.School of Mathematics and System Sciences,Shandong University,Jinan 250100,China 3.School of Mathematical Sciences,Nankai University,Tianjin 300071,China |
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| Abstract: | This paper introduces a method of bootstrap wavelet estimation in a nonparametric regression model with weakly dependent processes for both fixed and random designs. The asymptotic bounds for the bias and variance of the bootstrap wavelet estimators are given in the fixed design model. The conditional normality for a modified version of the bootstrap wavelet estimators is obtained in the fixed model. The consistency for the bootstrap wavelet estimator is also proved in the random design model. These results show that the bootstrap wavelet method is valid for the model with weakly dependent processes. |
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| Keywords: | Nonparametric regression weakly dependent process bootstrap wavelet |
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