Stochastic resonance in a statistical model of a time-integrating detector

We study an optimal nonparametric regression model for a threshold detector exposed to a noisy, subthreshold signal. The problem of recovering the signal is similar to that faced by neurons in nervous systems, although our model is intended to be normative rather than realistic. In our approach, the time-integrating activity of the neuron is modeled by kernel regression. Several aspects of the performance of the model are studied, including the existence of an optimal amount of noise (stochastic resonance). We construct a sequential, data-driven procedure for estimating the subthreshold signal. The performance of our model for threshold data is compared with kernel estimation for fully observed data. Finally, we discuss differences between our estimator and the best estimator for a constant signal.