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December 2015 Bootstrap and permutation tests of independence for point processes
Mélisande Albert, Yann Bouret, Magalie Fromont, Patricia Reynaud-Bouret
Ann. Statist. 43(6): 2537-2564 (December 2015). DOI: 10.1214/15-AOS1351

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 nonparametric 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. Wasserstein’s metric, which induces 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.

Citation

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Mélisande Albert. Yann Bouret. Magalie Fromont. Patricia Reynaud-Bouret. "Bootstrap and permutation tests of independence for point processes." Ann. Statist. 43 (6) 2537 - 2564, December 2015. https://doi.org/10.1214/15-AOS1351

Information

Received: 1 July 2014; Revised: 1 May 2015; Published: December 2015
First available in Project Euclid: 7 October 2015

zbMATH: 1327.62454
MathSciNet: MR3405603
Digital Object Identifier: 10.1214/15-AOS1351

Subjects:
Primary: 60F05 , 60G55 , 62E20 , 62F40 , 62M07
Secondary: 62P10

Keywords: $U$-statistics , bootstrap , Independence test , neuroscience , permutation , Point processes , Randomization , spike train analysis

Rights: Copyright © 2015 Institute of Mathematical Statistics

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Vol.43 • No. 6 • December 2015
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