论文标题
在标量 - 功能回归中选择功能协变量的导数
Selecting the Derivative of a Functional Covariate in Scalar-on-Function Regression
论文作者
论文摘要
本文提出了测试，以在标量 - 功能回归中使用功能协变量的不同衍生物在回归模型之间进行正式选择。我们证明，对于线性回归，使用不同衍生物的模型可以嵌套在模型中，该模型在观察到的函数的端点上包含点影响效应。然后可以使用对比度测试不同衍生物的规范。定义了非线性回归模型时，我们将应用$ J $测试来确定功能协变量和标量响应之间非线性结构的统计意义。这些方法的有限样本性能在模拟中得到了验证，并使用化学计量数据集证明了它们的实际应用。
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 defined, we apply a $J$ 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 a chemometric data set.
