BOOTSTRAP AND PERMUTATION TESTS OF INDEPENDENCE FOR POINT PROCESSES

• 成果类型: Article
• 署名作者: Albert, Melisande; Bouret, Yann; Fromont, Magalie; Reynaud-Bouret, Patricia
• 署名单位: Universite Cote d'Azur; Universite Cote d'Azur; Universite Rennes 2; Universite de Rennes
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/15-AOS1351
• 发表日期: 2015
• 页码: 2537-2564
• 关键词: high dimension; U-statistics; samples; events

摘要

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 resealed 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.