A novel method for testing the null hypothesis of no effect of a covariate on the response is proposed in functional linear concurrent regression. An equivalent random effects formulation of the functional regression model is established under which the testing problem reduces to testing for zero variance component for random effects. For this purpose, a one-sided score test approach is used, which is an extension of the classical score test. Theoretical justification is provided as to why the proposed testing procedure has the correct levels (asymptotically) under null using standard assumptions. Using numerical simulations, the testing method is shown to have the desired type I error rate and higher power compared to a bootstrapped F test currently existing in the literature. The model and the testing procedure give good performances even when the data are sparsely observed, and the functional covariate is contaminated with noise. Applications of the proposed testing method are demonstrated on gait data and a study of child mortality.

在函数线性并发回归中提出了一种用于检验协变量对响应没有影响的零假设的新方法。建立了函数回归模型的等效随机效应公式，在该公式下，测试问题简化为测试随机效应的零方差分量。为此，使用了单面分数测试方法，它是经典分数测试的扩展。提供了关于为什么建议的测试程序在使用标准假设的零下具有正确的水平（渐近地）的理论依据。使用数值模拟，与文献中目前存在的自举 F 测试相比，该测试方法显示出具有所需的 I 类错误率和更高的功效。即使在稀疏地观察数据并且函数协变量被噪声污染时，该模型和测试程序也能提供良好的性能。所提出的测试方法的应用在步态数据和儿童死亡率研究中得到证明。