Estimation Of Multivariate Shannon Entropy Using Moments

Three new entropy estimators of multivariate distributions are introduced. The two cases considered here concern when the distribution is supported by a unit sphere and by a unit cube. In the former case, the consistency and the upper bound of the absolute error for the proposed entropy estimator are established. In the latter one, under the assumption that only the moments of the underlying distribution are available, a non-traditional estimator of the entropy is suggested. We also study the practical performances of the constructed estimators through simulation studies and compare the estimators based on the moment-recovered approaches with their counterparts derived by using the histogram and kth nearest neighbour constructions. In addition, one worked example is briefly discussed.