🤖 AI Summary
This study addresses the lack of effective tests for independence and mean independence in weakly dependent data, such as sample paths from stationary ergodic stochastic processes. Building upon the Hilbert–Schmidt Independence Criterion, the authors develop a unified testing framework applicable to general topological spaces. Under near-epoch dependence (NED) conditions, they establish, for the first time, the consistency and asymptotic distribution theory of the test statistic under both fixed and local alternatives. By integrating kernel methods with asymptotic statistical analysis, the proposed approach substantially extends the scope of existing independence tests. Its favorable finite-sample performance is demonstrated through simulation studies on functional data.
📝 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.