Exponential Concentration of a Density Functional Estimator

03/28/2016

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by   Shashank Singh, et al.

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We analyze a plug-in estimator for a large class of integral functionals of one or more continuous probability densities. This class includes important families of entropy, divergence, mutual information, and their conditional versions. For densities on the d-dimensional unit cube [0,1]^d that lie in a β-Hölder smoothness class, we prove our estimator converges at the rate O ( n^-β/β + d). Furthermore, we prove the estimator is exponentially concentrated about its mean, whereas most previous related results have proven only expected error bounds on estimators.