Kernel-based independence and mean independence tests for weakly dependent data

TL;DR

This paper introduces a unified kernel-based framework for independence tests applicable to weakly dependent data, with theoretical analysis and simulation validation.

Contribution

It extends Hilbert-Schmidt independence tests to general topological spaces and analyzes their asymptotic behavior under dependence.

Findings

Test statistic is consistent under dependence.

Asymptotic distribution derived for stationary ergodic processes.

Simulation shows good finite-sample performance.

Abstract

We provide a unified framework for independence and mean independence tests based on the Hilbert-Schmidt independence criterion, extending some previous results in the literature to hold in general topological spaces. We also present a complete theoretical analysis of the test statistic asymptotic behavior when the observed sample corresponds to a partial sample path of some stationary and ergodic stochastic process under near epoch dependence assumptions. In particular, we explore the test statistic consistency and limit distribution under both fixed and local hypothesis. The finite sample performance of the test(s) is illustrated with a succinct simulation study involving functional data.