A Note on the Comparison of the Quadratic and Shannon's Mutual Information

The problem of estimating the information conveyed about a random variable by another one in a population on the basis of a sample drawn at random and with replacement from it was exhaustively analysed previously. From a theoretical viewpoint, this analysis showed the advantages of the quadratic mutual information against Shannon's mutual information in relation to such a problem. This theoretical conclusion is confirmed from an empirical viewpoint by comparing the population values and estimates for both information measures on the basis of samples obtained from a normal bivariate distribution by a Monte Carlo simulation.