Bootstrap and permutation tests of independence for point processes

Abstract : Motivated by a neuroscience question about synchrony detection in spike train analysis, we deal with the independence testing problem for point processes. We introduce non-parametric test statistics, which are rescaled general $U$-statistics, whose corresponding critical values are constructed from bootstrap and randomization/permutation approaches, making as few assumptions as possible on the underlying distribution of the point processes. We derive general consistency results for the bootstrap and for the permutation w.r.t. to Wasserstein's metric, which induce weak convergence as well as convergence of second order moments. The obtained bootstrap or permutation independence tests are thus proved to be asymptotically of the prescribed size, and to be consistent against any reasonable alternative. A simulation study is performed to illustrate the derived theoretical results, and to compare the performance of our new tests with existing ones in the neuroscientific literature.
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The Annals of Statistics, Institute of Mathematical Statistics, 2015, 43 (6), pp.2537-2564. <10.1214/15-AOS1351>
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https://hal.archives-ouvertes.fr/hal-01001984
Contributeur : Mélisande Albert <>
Soumis le : mercredi 27 mai 2015 - 14:49:07
Dernière modification le : jeudi 23 février 2017 - 14:07:14
Document(s) archivé(s) le : mardi 15 septembre 2015 - 07:00:45

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Mélisande Albert, Yann Bouret, Magalie Fromont, Patricia Reynaud-Bouret. Bootstrap and permutation tests of independence for point processes. The Annals of Statistics, Institute of Mathematical Statistics, 2015, 43 (6), pp.2537-2564. <10.1214/15-AOS1351>. <hal-01001984v4>

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