Asymptotically Optimal Nonparametric Classification Rules for Spike Train Data

Spike train data find a growing list of applications in computational neuroscience, streaming data and finance. Statistical analysis of spike trains is based on various probabilistic and neural network models. The statistical approach relies on parametric or nonparametric specifications of the underlying model. In this paper we consider the nonparametric classification problem for a class of spike train data characterized by nonparametricaly specified intensity functions. We derive the optimal Bayes rule and next formulate the plug-in non-parametric kernel classifiers. Asymptotical properties of the rules are established including the limit with respect to the increasing observation time interval and the size of a training set. The obtained results are supported by a finite sample simulation studies.