No matter the nature of the response and/or explanatory variables in a regression model, some basic issues such as the existence of an effect of the predictor on the response, or the assessment of a common shape across groups of observations, must be solved prior to model fitting. This is also the case for regression models involving circular variables (supported on the unit circumference). In that context, using kernel regression methods, this paper provides a flexible alternative for constructing pilot estimators that allow to construct suitable statistics to perform no-effect tests and tests for equality and parallelism of regression curves. Finite sample performance of the proposed methods is analyzed in a simulation study and illustrated with real data examples.

中文翻译：

---

循环回归的非参数检验

无论回归模型中的响应和/或解释变量的性质如何，必须先解决一些基本问题，例如预测变量对响应的影响，或对不同观测组的共同形状的评估模型拟合。对于涉及圆形变量（单位周长支持）的回归模型也是如此。在这种情况下，本文使用核回归方法为构建试点估计量提供了一种灵活的替代方案，允许构建合适的统计量来执行无影响测试以及回归曲线的相等性和平行性的测试。在模拟研究中分析了所提出方法的有限样本性能，并用真实数据示例进行了说明。