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Article Dans Une Revue Journal of Mathematical Neuroscience Année : 2014

Goodness-of-Fit Tests and Nonparametric Adaptive Estimation for Spike Train Analysis

Résumé

When dealing with classical spike train analysis, the practitioner often per-forms 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 (Yana et al. in Bio-phys.. 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 un-desirable 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 consis-tent with a controlled rate of convergence. Some nonparametric estimates satisfying those constraints in the Poisson or in the Hawkes framework are highlighted. More-over, 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 com-plete analysis with these tools on single unit activity recorded on a monkey during a sensory-motor task. Electronic supplementary material The online version of this article (doi:10.1186/2190-8567-4-3) contains supplementary material.
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Dates et versions

hal-01100718 , version 1 (09-01-2015)

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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, 2014, 4, pp.3 - 330325. ⟨10.1109/TIT.1981.1056305⟩. ⟨hal-01100718⟩
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