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Restricted likelihood ratio tests for linearity in scalar-on-function regression

机译：标量函数回归中线性的受限似然比检验

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摘要

We propose a procedure for testing the linearity of a scalar-on-function regression relationship. To do so, we use the functional generalized additive model (FGAM), a recently developed extension of the functional linear model. For a functional covariate , the FGAM models the mean response as the integral with respect to of where is an unknown bivariate function. The FGAM can be viewed as the natural functional extension of generalized additive models. We show how the functional linear model can be represented as a simple mixed model nested within the FGAM. Using this representation, we then consider restricted likelihood ratio tests for zero variance components in mixed models to test the null hypothesis that the functional linear model holds. The methods are general and can also be applied to testing for interactions in a multivariate additive model or for testing for no effect in the functional linear model. The performance of the proposed tests is assessed on simulated data and in an application to measuring diesel truck emissions, where strong evidence of nonlinearities in the relationship between the functional predictor and the response are found.
机译：我们提出了一个程序来测试标量函数回归关系的线性。为此，我们使用功能广义加性模型（FGAM），它是功能线性模型的最新开发。对于函数协变量，FGAM将平均响应建模为关于未知双变量函数的整数。 FGAM可以看作是广义加性模型的自然功能扩展。我们展示了如何将函数线性模型表示为嵌套在FGAM中的简单混合模型。然后使用这种表示法，考虑混合模型中零方差分量的受限似然比检验，以检验功能线性模型成立的原假设。该方法是通用的，还可以用于测试多元加性模型中的相互作用或用于测试功能线性模型中的无影响。拟议测试的性能通过模拟数据进行评估，并用于测量柴油卡车的排放，其中发现了功能预测变量与响应之间的非线性关系的有力证据。

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