A new RKHS-based global testing for functional linear model

Abstract: This article studies global testing of the slope function in functional linear regression model in the framework of reproducing kernel Hilbert space. We propose a new testing statistic based on smoothness regularization estimators. The asymptotic distribution of the testing statistic is established under null hypothesis. It is shown that the null asymptotic distribution is determined jointly by the reproducing kernel and the covariance function. Our theoretical analysis shows that the proposed testing is consistent over a class of smooth local alternatives. Despite the generality of the method of regularization, we show the procedure is easily implementable. Numerical examples are provided to demonstrate the empirical advantages over the competing methods.