Bias analysis in entropy estimation

Abstract: We consider the problem of finite sample corrections for entropy estimation. New estimates of the Shannon entropy are proposed and their systematic error (the bias) is computed analytically. We find that our results cover correction formulas of current entropy estimates recently discussed in literature. The trade-off between bias reduction and the increase of the corresponding statistical error is analyzed. PACS: 89.70+c, 02.50.Fz, 05.45.Tp Statistical fluctuations of small samples induce both statistical and systematic deviations of entropy estimates. In the naive (”likelihood”) estimator one replaces the discrete probabilities pi, for i = 1,..., M, in the Shannon entropy 1