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

Summary 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.