On Estimating L_2^2 Divergence

10/30/2014

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by   Akshay Krishnamurthy, et al.

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We give a comprehensive theoretical characterization of a nonparametric estimator for the L_2^2 divergence between two continuous distributions. We first bound the rate of convergence of our estimator, showing that it is √(n)-consistent provided the densities are sufficiently smooth. In this smooth regime, we then show that our estimator is asymptotically normal, construct asymptotic confidence intervals, and establish a Berry-Esséen style inequality characterizing the rate of convergence to normality. We also show that this estimator is minimax optimal.