Estimation of mutual information using kernel density estimators

Mutual information is useful for investigating the dependence between two experimental time series. It is often used to establish an appropriate time delay in phase-portrait reconstruction from time-series data. A histogram based approach has been used so far to estimate the probabilities. It is shown here that kernel density estimation of the probability density functions needed in estimating the average mutual information across two coordinates can be more effective than the histogram method of Fraser and Swinney [Phys. Rev. A 33, 1134 (1986)].