A new class of entropy estimators for multi-dimensional densities

We present a new class of estimators for approximating the entropy of multi-dimensional probability densities based on a sample of the density. These estimators extend the classic "m-spacing" estimators of Vasicek (1976) and others for estimating entropies of one-dimensional probability densities. Unlike plug-in estimators of entropy, which first estimate a probability density and then compute its entropy. our estimators avoid the difficult intermediate step of density estimation. For fixed dimension. the estimators an polynomial in the sample size. Similarities to consistent and asymptotically efficient one-dimensional estimators of entropy suggest that our estimators may sham these properties.