Kernel-based method for joint independence of functional variables

TL;DR

This paper introduces a kernel-based statistical test for assessing the joint independence of multiple functional variables, extending the HSIC method to handle more than two variables with proven asymptotic properties.

Contribution

It proposes a generalized $d$HSIC estimator for testing joint independence among multiple functional variables, with established asymptotic normality under both hypotheses.

Findings

The proposed test performs well in finite samples.

Asymptotic normality is proven under both hypotheses.

Simulation results demonstrate good performance.

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 ($d$HSIC) which generalizes HSIC for the case where $d \geq 2$. We then get asymptotic normality of this estimator both under joint independence hypothesis and under the alternative hypothesis. A simulation study shows good performance of the proposed test on finite sample.