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# 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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https://hal.archives-ouvertes.fr/hal-01001984
Contributor : Mélisande Albert Connect in order to contact the contributor
Submitted on : Wednesday, May 27, 2015 - 2:49:07 PM
Last modification on : Friday, May 20, 2022 - 9:04:48 AM
Long-term archiving on: : Tuesday, September 15, 2015 - 7:00:45 AM

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

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