  We propose a novel method for testing the null hypothesis of no effect of a
covariate on the response in the context of functional linear concurrent
regression. We establish an equivalent random effects formulation of our
functional regression model under which our testing problem reduces to testing
for zero variance component for random effects. For this purpose, we use a
one-sided score test approach, which is an extension of the classical score
test. We provide theoretical justification as to why our testing procedure has
the right levels (asymptotically) under null using standard assumptions. Using
numerical simulations, we show that our testing method has the desired type I
error rate and gives higher power compared to a bootstrapped F test currently
existing in the literature. Our model and testing procedure are shown to give
good performances even when the data is sparsely observed, and the covariate is
contaminated with noise. Applications of the proposed testing method are
demonstrated on gait study and a dietary calcium absorption data.
