| 函数系数线性自回归模型的样条估计 |
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| 引用本文： | 武新乾,田铮,李小斌.函数系数线性自回归模型的样条估计[J].数学研究及应用,2007,27(4):869-875. |
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| 作者姓名： | 武新乾 田铮 李小斌 |
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| 作者单位： | 1. 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;模式识别国家重点实验室,中科院自动化所,北京,100080 |
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| 基金项目： | 国家自然科学基金;航空基础科学基金 |
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| 摘 要： | 基于多项式样条全局光滑方法,建立函数系数线性自回归模型中系数函数的样条估计.在适当条件下,证明了系数函数多项式样条估计的相合性,并给出了它们的收敛速度.模拟例子验证了理论结果的正确性.
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| 关 键 词： | 函数系数线性自回归模型 多项式样条估计 相合性 收敛速度. |
| 文章编号： | 1000-341X（2007）04-0869-07 |
| 收稿时间： | 2005/9/21 0:00:00 |
| 修稿时间： | 2005-09-21 |
Spline Estimates in Functional-Coefficient Linear Autoregressive Models |
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| WU Xin-qian,TIAN Zheng and LI Xiao-bin.Spline Estimates in Functional-Coefficient Linear Autoregressive Models[J].Journal of Mathematical Research with Applications,2007,27(4):869-875. |
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| Authors: | WU Xin-qian TIAN Zheng and LI Xiao-bin |
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| Institution: | Department of Applied Mathematics, Northwestern Polytechnical University, Shaanxi 710072, China;Department of Applied Mathematics, Northwestern Polytechnical University, Shaanxi 710072, China; National Key Laboratory of Pattern Recognition, \& Institute of Automation, Chinese Academy of Sciences, Beijing 100080, China;Department of Applied Mathematics, Northwestern Polytechnical University, Shaanxi 710072, China |
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| Abstract: | A global smoothing method based on polynomial splines is used to estimate the coefficient functions in functional-coefficient linear autoregressive models.Under some mild conditions,consistency of the polynomial spline estimators is proved.Rates of convergence of these estimators are also given. The main results are verified by a simulation example. |
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| Keywords: | functional-coefficient linear autoregressive model polynomial spline estimation consistency convergence rate |
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