Estimation of the entropy on the basis of its polynomial representation

An algorithm for estimating the entropy, which is based on the representation of the entropy function as the sum of two polynomial terms, called the polynomial approximation function and the remainder, is proposed. We construct an accurate and unbiased estimate of the value of the polynomial approximation function and use the known Bayesian approach to estimate the remainder. The combined estimator essentially reduces the bias of the constructed estimate as compared to the known estimators. Simulation results that confirm the claim are presented.