识别两条回归曲线之间的偏移
Identifying shifts between two regression curves
摘要：
本文研究了两个凸（凹）回归函数在两个样本中的响应和协变量之间的关系是否因水平和/或垂直轴的移动而不同的问题。我们考虑一个非参数的情况下，假设只有光滑的回归函数。一个图形工具的基础上的衍生物的回归函数及其逆提出了回答这个问题，并研究了几个例子。我们还正式提出了相应的假设，并开发了一个统计检验这个问题。在原假设和局部替换下，研究了相应检验统计量的渐近性质。与大多数关于比较形状不变模型的文献相反，这需要独立的数据，该过程适用于依赖和非平稳数据。我们还通过一个小的模拟研究和一个真实数据的例子说明了新的测试的有限样本性质。
英文摘要：
This article studies the problem whether two convex (concave) regression functions modelling the relation between a response and covariate in two samples differ by a shift in the horizontal and/or vertical axis. We consider a nonparametric situation assuming only smoothness of the regression functions. A graphical tool based on the derivatives of the regression functions and their inverses is proposed to answer this question and studied in several examples. We also formalize this question in a corresponding hypothesis and develop a statistical test. The asymptotic properties of the corresponding test statistic are investigated under the null hypothesis and local alternatives. In contrast to most of the literature on comparing shape invariant models, which requires independent data the procedure is applicable for dependent and non-stationary data. We also illustrate the finite sample properties of the new test by means of a small simulation study and a real data example.
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