This paper focuses on the problem of testing the null hypothesis that the regression functions of several populations are equal under a general nonparametric homoscedastic regression model. To protect against atypical observations, the test statistic is based on the residuals obtained by using a robust estimate for the regression function under the null hypothesis. The asymptotic distribution of the test statistic is studied under the null hypothesis and under root$-n$ contiguous alternatives. A Monte Carlo study is performed to compare the finite sample behaviour of the proposed tests with the classical one obtained using local averages. An illustration to a real data set is also provided.
翻译:本文着重探讨在一般非对称同质回归模型下若干人口的回归功能平等这一无效假设的检验问题。为了防范非典型的观察,测试统计数据依据的是在无效假设下对回归功能进行可靠估计后获得的残留物。测试统计数据的无症状分布根据无效假设和根值-美元毗连替代物进行研究。开展蒙特卡洛研究,将拟议测试的有限样本行为与使用当地平均数获得的典型样本行为进行比较。还提供了真实数据集的示例。