Noise can linearize the firing-rate curve by removing the discontinuity at spike threshold, dampen resonance effects [14], reducing network synchronization [22], and dynamically amplify an embedded signal through stochastic resonance [23], [24] or some of its generalizations [25].
Subsequent analyses have turned up a discontinuity at various thresholds (though other papers have not).
But, as shown here, the discontinuity structure of the threshold itself supplies identifying information for the parametric coefficients without the need for extra randomness in the regressors.
Using a novel data set of the students who entered high school from 2006 to 2008 in a Chinese city, our fuzzy regression discontinuity estimates exploit the threshold values of the high school entrance exam scores.
The discontinuities near the thresholds arise because Youden's index is used to set the classification thresholds for the individual networks.
Two different estimation strategies are used: regression discontinuity design exploiting age thresholds above which fees are charged, and difference-in-differences models exploiting policy changes.
To provide statistical inferences on the presence of discontinuities at the eligibility threshold, we estimate a series of parametric models (Table 2).
Alternatively, one may stop the simulation as soon as the solution hits the jump discontinuity, i.e. the threshold value for firing.
We find that there is a sharp and economically-significant discontinuity around the zero-earnings threshold in the level of debt issues.
Models based on voting that are built on unbalanced data sets and use Youden's index as the criterion for setting individual network classification thresholds tend to have a discontinuity in observed error rates near the ensemble voting threshold.
