Kernel-based method for joint independence of functional variables

Abstract

This work investigates the problem of testing whether d functional random variables are jointly independent, using a modified estimator of the d-variable Hilbert Schmidt Indepedence Criterion (dHSIC). We then get the asymptotic normality of this estimator both under the joint independence hypothesis and under the alternative hypothesis. A simulation study shows the good performance of the proposed test on a finite sample.