Robust hypothesis testing in functional linear models

We extend three robust tests - Wald-type, the likelihood ratio-type and F-type in functional linear models with the scalar dependent variable and the functional covariate. Based on the percentage of variance explained criterion, we use the functional principal components analysis and re-express a functional linear model to a finite regression. We investigate the theoretical properties of these robust testing procedures and assess the finite sample properties through the numerical simulation. In our experiments, the power performance and Type I error rates are studied separately in the sparsely and densely functional linear models. The simulation results show that the robust test procedures are more stable and less sensitive to heavy-tailed distributed errors than the classical ones. Two real datasets are analysed to compare the classical and robust testing procedures.