Asymptotic properties of sample-based entropy, information divergence, and related metrics

Summary form only given. Given a sample produced by an unknown memoryless source, we show how to estimate its entropy with much higher precision by adding a simple correction term to a commonly used expression. We also derive asymptotic expansions for sample-based entropy of mixtures and sample-based mutual information. These results are obtained using technique discussed by P. Flajolet (see Theoretical Computer Science, vol.215, p.371-81, 1999).