The mutual information. Estimation in the sampling without replacement
Marı́a Ángeles Gil, Rigoberto Pérez, Pedro Gil · Czech digital mathematics library · 1987
In previous papers, the "mutual information of order fi concerning two random variables" was defined from the concept of conditional entropy of order p (Z. Dar6czy, 1970).The aim of the present paper is to approach the value of the mutual information of order $ = 2 in a large population on the basis of a sample drawn at random and without replacement from it.This purpose is achieved by obtaining an unbiased estimator of that value and estimating its mean square error.In addition, a contrast between samplings with and without replacement shows that the second one entails an improvement in the estimation precision with respect to the first one.Finally, we discuss the suitability of adopting the measure of order p = 2 against Shannon's amount of information.