124
92

Nonparametric Estimation of Renyi Divergence and Friends

Abstract

We consider nonparametric estimation of L_2, Renyi-α\alpha and Tsallis-α\alpha divergences of continuous distributions. Our approach is to construct estimators for particular integral functionals of two densities and translate them into divergence estimators. For the integral functionals, our estimators are based on corrections of a preliminary plug-in estimator. We analyze the rates of convergence for our estimators and show that the parametric rate of n1/2n^{-1/2} is achievable when the densities' smoothness s are both at least d/4d/4 where dd is the dimension. We also derive minimax lower bounds for this problem which confirm that s>d/4s > d/4 is necessary to achieve the n1/2n^{-1/2} rate of convergence. We confirm our theoretical guarantees with a number of simulations.

View on arXiv
Comments on this paper