Goodness-of-fit tests and nonparametric adaptive estimation for spike train analysis

Abstract : When dealing with classical spike train analysis, the practitioner often performs goodness-of-fit tests to test whether the observed process is a Poisson process, for instance, or if it obeys another type of probabilistic model. In doing so, there is a fundamental plug-in step, where the parameters of the supposed underlying model are estimated. The aim of this article is to show that plug-in has sometimes very undesirable effects. We propose a new method based on subsampling to deal with those plug-in issues in the case of the Kolmogorov- Smirnov test of uniformity. The method relies on the plug-in of good estimates of the underlying model, that have to be consistent with a controlled rate of convergence. Some non parametric estimates satisfying those constraints in the Poisson or in the Hawkes framework are highlighted. Moreover they share adaptive properties that are useful from a practical point of view. We show the performance of those methods on simulated data. We also provide a complete analysis with these tools on single unit activity recorded on a monkey during a sensory-motor task.
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Patricia Reynaud-Bouret, Vincent Rivoirard, Franck Grammont, Christine Tuleau-Malot. Goodness-of-fit tests and nonparametric adaptive estimation for spike train analysis. Journal of Mathematical Neuroscience, BioMed Central, 2014, pp.4:3. ⟨10.1186/2190-8567-4-3⟩. ⟨hal-00789127v2⟩

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