Statistical Analysis of Stochastic Resonance in a Thresholded Detector
DOI:
https://doi.org/10.17713/ajs.v32i1&2.449Abstract
A subthreshold signal may be detected if noise is added to the data. The noisy signal must be strong enough to exceed the threshold at least occasionally; but very strong noise tends to drown out the signal. There is an optimal noise level, called stochastic resonance. We explore the detectability of different signals, using statistical detectability measures.
In the simplest setting, the signal is constant, noise is added in the form of i.i.d. random variables at uniformly spaced times, and the detector records the times at which the noisy signal exceeds the threshold. We study the best estimator for the signal from the thresholded data and determine optimal configurations of several detectors with different thresholds.
In a more realistic setting, the noisy signal is described by a nonparametric regression model with equally spaced covariates and i.i.d. errors, and the detector records again the times at which the noisy signal exceeds the threshold. We study Nadaraya–Watson kernel estimators from thresholded data. We determine the asymptotic mean squared error and the asymptotic mean average squared error and calculate the corresponding local and global optimal bandwidths. The minimal asymptotic mean average squared error shows a strong stochastic resonance effect.
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