Kernel-based independence and mean independence tests for weakly dependent data
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917451384487936 |
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| author | Diz-Castro, Daniel Febrero-Bande, Manuel González-Manteiga, Wenceslao |
| author_facet | Diz-Castro, Daniel Febrero-Bande, Manuel González-Manteiga, Wenceslao |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_28104 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Kernel-based independence and mean independence tests for weakly dependent data Diz-Castro, Daniel Febrero-Bande, Manuel González-Manteiga, Wenceslao Methodology Statistics Theory 62G10 (Primary) 62G09, 62G20 (Secondary) 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. |
| title | Kernel-based independence and mean independence tests for weakly dependent data |
| topic | Methodology Statistics Theory 62G10 (Primary) 62G09, 62G20 (Secondary) |
| url | https://arxiv.org/abs/2604.28104 |