Testing independence of functional variables by an Hilbert-Schmidt independence criterion estimator

TL;DR

This paper introduces a new Hilbert-Schmidt Independence Criterion estimator, establishes its asymptotic properties, and develops a novel independence test for variables in metric spaces, supported by simulation comparisons.

Contribution

It presents a modified estimator for HSIC, proves its asymptotic normality, and introduces a new independence test for metric space-valued variables.

Findings

The estimator is asymptotically normal under independence and dependence.

The new test effectively detects independence in metric space-valued variables.

Simulation results compare favorably with existing methods.

Abstract

We propose an estimator of the Hilbert-Schmidt Independence Criterion obtained from an appropriate modification of the usual estimator. We then get asymptotic normality of this estimator both under independence hypothesis and under the alternative hypothesis. A new test for independence of random variables valued into metric spaces is then introduced, and a simulation study that allows to compare the proposed test to an existing one is provided