随机设计下非参数回归模型方差变点检验

Test for the variance change in nonparametric regression model in a random design

目的研究随机设计下非参数回归模型方差变点检验。方法用局部多项式方法估计回归曲线得到残差序列,基于残差序列的平方构造CUSUM检验统计量,推导检验统计量的极限分布。结果在一定条件下证明了原假设下检验统计量收敛于Brown桥的上确界。结论局部多项式方法同时适用于随机设计与固定设计数值,方法性是有效性的。

Aim To test the variance change in nonparametric regression model in a random design.Methods The residual sequence is obtained by local linear methods and the CUSUM of squares test statistics is established based on the square of residual.Results It is shown that under certain conditions,the distribution of the test statistics converges at the supremum of a standard Brown bridge.Conclusion Local linear model can be used in random design and fixed dosign.The method turns out to be effective after being tested on simulated examples.