This paper presents tests to formally choose between regression models using different derivatives of a functional covariate in scalar-on-function regression. We demonstrate that for linear regression, models using different derivatives can be nested within a model that includes point-impact effects at the end-points of the observed functions. Contrasts can then be employed to test the specification of different derivatives. When nonlinear regression models are employed, we apply a C test to determine the statistical significance of the nonlinear structure between a functional covariate and a scalar response. The finite-sample performance of these methods is verified in simulation, and their practical application is demonstrated using both chemometric and environmental data sets.

本文介绍了在标量函数回归中使用函数协变量的不同导数在回归模型之间进行正式选择的测试。我们证明，对于线性回归，使用不同导数的模型可以嵌套在一个模型中，该模型包括观察函数端点处的点冲击效应。然后可以使用对比来测试不同导数的规范。当采用非线性回归模型时，我们应用C检验来确定函数协变量和标量响应之间的非线性结构的统计显着性。在模拟中验证了这些方法的有限样本性能，并使用化学计量学和环境数据集证明了它们的实际应用。