Convergence Properties of Some Spike-Triggered Analysis Techniques

All of our results are obtained in the setting of a (possibly multidimensional) linear-nonlinear (LN) cascade model for stimulus-driven neural activity. We start by giving exact rate of convergence results for the common spike-triggered average (STA) technique. Next, we analyze a spike-triggered covariance method, variants of which have been recently exploited successfully by Bialek, Simoncelli, and colleagues. These first two methods suffer from extraneous conditions on their convergence; therefore, we introduce an estimator for the LN model parameters which is designed to be consistent under general conditions. We provide an algorithm for the computation of this estimator and derive its rate of convergence. We close with a brief discussion of the efficiency of these estimators and an application to data recorded from the primary motor cortex of awake, behaving primates.