# A Score Based Test for Functional Linear Concurrent Regression

## TL;DR

This paper introduces a new score-based test for assessing the effect of covariates in functional linear concurrent regression, offering improved power and robustness over existing methods, with theoretical and empirical validation.

## Contribution

It develops a novel score test for zero variance components in functional regression, with theoretical justification and superior performance demonstrated through simulations and real data applications.

## Key findings

- Test maintains correct type I error rate.
- Achieves higher power than bootstrapped F test.
- Performs well with sparse and noisy data.

## Abstract

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.