中文摘要：

研究随机设计下非参数回归模型方差变点Ratio检验．首先用局部多项式方法估计回归曲线得到残差序列，其次基于残差的平方序列构造Ratio检验统计量并推导检验统计量的极限分布．最后数值模拟与实例分析结果表明方法的有效性．

英文摘要：

This paper considers the detection problem of variance change point in nonparametric regression model under random design. The residual sequence is obtained by local linear method and the ratio test statistics is established based on the residual squares sequences. The limiting distribution of the test statistic is established. The method turns out to be effective after being tested on simulated examples and applied to Motorcycle data.