A Score Based Test for Functional Linear Concurrent Regression

Abstract 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.