| 随机设计下回归函数模型变点的小波估计 |
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| 引用本文： | 赵云石,朱永忠. 随机设计下回归函数模型变点的小波估计[J]. 济南大学学报(自然科学版), 2012, 26(2): 195-198 |
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| 作者姓名： | 赵云石 朱永忠 |
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| 作者单位： | 河海大学理学院,江苏南京,210098 |
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| 基金项目： | 国家自然科学基金﹙50979029﹚ |
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| 摘 要： | 研究在随机设计下对含有单个跳跃点的回归函数的小波估计。将随机设计通过变换转换成等距设计，在等距设计下利用单个跳跃点和跳跃度的估计量，构造出含有单个变点的回归函数估计。数值分析比较结果显示：该方法不仅保持了尖点附近的良好性质，而且在跳跃点附近也有效地避免了吉布斯现象。
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| 关 键 词： | 随机设计 严格变点问题 回归模型 收敛性 小波函数估计 |
Wavelet Estimation of Change Points in Regression Function Models under Random Design |
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| ZHAO Yun-shi , ZHU Yong-zhong. Wavelet Estimation of Change Points in Regression Function Models under Random Design[J]. Journal of Jinan University(Science & Technology), 2012, 26(2): 195-198 |
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| Authors: | ZHAO Yun-shi ZHU Yong-zhong |
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| Affiliation: | (Hohai University,College of Science,Nanjing 210098,China) |
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| Abstract: | This article discusses the wavelet estimation of a regression function with single jump point under random designs.Dealing with a random design,we first transform it to an equispaced design.By using estimators of single jump and a jump size,the estimator of a regression function which may contain a single jump point is obtained.Therefore,the proposed estimator keeps the adaptive properties of wavelet estimators around cusp points,and reduces the Gibbs phenomenon more efficiently around a jump point. |
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| Keywords: | random design sharp change point problem regression model convergence wavelet function estimation |
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