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BOOTSTRAP AND PERMUTATION TESTS OF INDEPENDENCE FOR POINT PROCESSES
, 2015
"... 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 Ustatistics, whose corresponding critical values are constructed from boo ..."
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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 Ustatistics, 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 secondorder 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.
CONCENTRATION INEQUALITIES, COUNTING PROCESSES AND ADAPTIVE STATISTICS ∗
"... Abstract. Adaptive statistics for counting processes need particular concentration inequalities to define and calibrate the methods as well as to precise the theoretical performance of the statistical inference. The present article is a small (non exhaustive) review of existing concentration inequal ..."
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Abstract. Adaptive statistics for counting processes need particular concentration inequalities to define and calibrate the methods as well as to precise the theoretical performance of the statistical inference. The present article is a small (non exhaustive) review of existing concentration inequalities that are useful in this context. Résumé. Les statistiques adaptatives pour les processus de comptage nécessitent des inégalités de concentration particulières pour définir et calibrer les méthodes ainsi que pour comprendre les performances de l’inférence statistique. Cet article est une revue non exhaustive des inégalités de concentration qui sont utiles dans ce contexte.