Estimating Functions of Probability Distributions from a Finite Set of   Samples, Part 1: Bayes Estimators and the Shannon Entropy
  We present estimators for entropy and other functions of a discrete probability distribution when the data is a finite sample drawn from that probability distribution. In particular, for the case when the probability distribution is a joint distribution, we present finite sample estimators for the mutual information, covariance, and chi-squared functions of that probability distribution. 
David H. Wolpert, David R. Wolf