非参数回归模型均值函数结构变点的检测与应用

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.

Detection and applications of structural breaks of mean function in nonparametric regression models

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.