Estimating the number of neurons in multi-neuronal spike trains

A common way of studying the relationship between neural activity and behavior is through the analysis of neuronal spike trains that are recorded using one or more electrodes implanted in the brain. Each spike train typically contains spikes generated by multiple neurons. A natural question that arises is "what is the number of neurons $\nu$ generating the spike train?"; This article proposes a method-of-moments technique for estimating $\nu$. This technique estimates the noise nonparametrically using data from the silent region of the spike train and it applies to isolated spikes with a possibly small, but nonnegligible, presence of overlapping spikes. Conditions are established in which the resulting estimator for $\nu$ is shown to be strongly consistent. To gauge its finite sample performance, the technique is applied to simulated spike trains as well as to actual neuronal spike train data.