引用本文:田铮,赵春辉,陈占寿.非参数回归模型均值函数结构变点的检测与应用[J].控制理论与应用,2011,28(3):351~357.[点击复制]
TIAN Zheng,ZHAO Chun-hui,CHEN Zhan-shou.Detection and applications of structural breaks of mean function in nonparametric regression models[J].Control Theory and Technology,2011,28(3):351~357.[点击复制]
非参数回归模型均值函数结构变点的检测与应用
Detection and applications of structural breaks of mean function in nonparametric regression models
摘要点击 2275  全文点击 1961  投稿时间：2009-10-23  修订日期：2010-04-15
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DOI编号  10.7641/j.issn.1000-8152.2011.3.CCTA091338
  2011,28(3):351-357
中文关键词  非参数模型  均值函数  结构变点  核估计  Bootstrap检验
英文关键词  nonparametric model  mean function  structural break  kernel estimation  Bootstrap test
基金项目  国家自然科学基金资助项目(10926197, 60972150); 西北工业大学科技创新基金资助项目(2007KJ01033).
作者单位E-mail
田铮 西北工业大学 应用数学系
中国科学院 遥感应用研究所遥感科学国家重点实验室 		 
赵春辉* 西北工业大学 应用数学系 zc3h@sina.com 
陈占寿 西北工业大学 应用数学系  
中文摘要
      本文将一类系统参数变点检测问题转化为非参数回归模型均值函数结构变点的检测问题. 针对当非参数模型均值函数跃度的长期均值为零时, 残量累积和(cumulative sum, CUSUM)统计量无效的问题, 首先利用均值函数的核估计构造新统计量, 给出了原假设和备择假设下统计量的极限分布; 进一步构造Bootstrap检验, 证明了Bootstrap检验的一致性; 最后以模拟结果表明新方法明显优于已有的方法, 并应用于两类实际数据分析, 说明方法的有效性.
英文摘要
      The detection of parametric change is transformed into the detection of structural breaks of mean function in the nonparametric models. For the residual cumulative sum(CUSUM) test becomes invalid when the long rang average of jump of the mean function is zero, a new statistic is built based on the kernel estimation of the mean function, and the limiting distributions of null hypothesis and alternative hypothesis are obtained. A Bootstrap procedure is proposed and the consistency of the test is also proved. Finally, simulation and real data analysis are performed to investigate the finite sample properties of our approach. Results show that our method is more powerful than methods proposed in reference.