  A non-parametric k-nearest neighbour based entropy estimator is proposed. It
improves on the classical Kozachenko-Leonenko estimator by considering
non-uniform probability densities in the region of k-nearest neighbours around
each sample point. It aims at improving the classical estimators in three
situations: first, when the dimensionality of the random variable is large;
second, when near-functional relationships leading to high correlation between
components of the random variable are present; and third, when the marginal
variances of random variable components vary significantly with respect to each
other. Heuristics on the error of the proposed and classical estimators are
presented. Finally, the proposed estimator is tested for a variety of
distributions in successively increasing dimensions and in the presence of a
near-functional relationship. Its performance is compared with a classical
estimator and shown to be a significant improvement.
