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arXiv · 1907.00196

Statistical estimation of the Kullback-Leibler divergence

Alexander Bulinski·Denis Dimitrov
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Abstract

Wide conditions are provided to guarantee asymptotic unbiasedness and L^2-consistency of the introduced estimates of the Kullback-Leibler divergence for probability measures in R^d having densities w.r.t. the Lebesgue measure. These estimates are constructed by means of two independent collections of i.i.d. observations and involve the specified k-nearest neighbor statistics. In particular, the established results are valid for estimates of the Kullback-Leibler divergence between any two Gaussian measures in R^d with nondegenerate covariance matrices. As a byproduct we obtain new statements concerning the Kozachenko-Leonenko estimators of the Shannon differential entropy.

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Alexander Bulinski, Denis Dimitrov. 2019-06-29. Statistical estimation of the Kullback-Leibler divergence. https://arxiv.org/abs/1907.00196

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