An Optimal Entropy Estimator which is an Average over Plural Independent Estimates

Abstract

We cannot record biological signals, e.g., neural signals, over long time, because of biological tiredness and adaptation property. We often adopt the average over plural estimates obtained from samples recorded in different trials as a final estimate to improve the estimation accuracy. For minimizing mean squared error of the entropy estimation, we should optimally balance between bias error and mean squared error of individual estimations, however the optimal balance is unknown. This paper derivates the optimal balance between bias error and mean squared error of individual estimations.