A scalar-response functional model describes the association between a scalar response and a set of functional covariates. An important problem in the functional data literature is to test nullity or linearity of the effect of the functional covariate in the context of scalar-on-function regression. This article provides an overview of the existing methods for testing both the null hypotheses that there is no relationship and that there is a linear relationship between the functional covariate and scalar response, and a comprehensive numerical comparison of their performance. The methods are compared for a variety of realistic scenarios: when the functional covariate is observed at dense or sparse grids and measurements include noise or not. Finally, the methods are illustrated on the Tecator data set.

中文翻译：

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标量函数回归中测试方法的比较

标量响应功能模型描述了标量响应和一组功能协变量之间的关联。功能数据文献中的一个重要问题是在标量对函数回归的背景下测试功能协变量的影响的无效性或线性。本文概述了现有的方法，这些方法用于检验函数协变量和标量响应之间不存在关系以及线性关系的原假设，并对其性能进行全面的数值比较。在各种现实情况下对这些方法进行了比较：当在密集或稀疏的网格上观察到函数协变量，并且测量结果是否包含噪声时。最后，在Tecator数据集上说明了这些方法。