An independence test for functional variables based on kernel normalized cross-covariance operator

TL;DR

This paper introduces a new statistical test for independence of functional variables based on kernel methods, with proven asymptotic properties and comparative simulation results.

Contribution

It develops a novel independence test for functional data using normalized cross-covariance operators and establishes its asymptotic normality.

Findings

The test achieves accurate independence detection in simulations.

It outperforms some existing methods in power and size.

Asymptotic normality is proven under the null hypothesis.

Abstract

We propose an independence test for random variables valued into metric spaces by using a test statistic obtained from appropriately centering and rescaling the squared Hilbert-Schmidt norm of the usual empirical estimator of normalized cross-covariance operator. We then get asymptotic normality of this statistic under independence hypothesis, so leading to a new test for independence of functional random variables. A simulation study that allows to compare the proposed test to existing ones is provided.