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arXiv · 1410.8372

On Estimating $L_2^2$ Divergence

Akshay Krishnamurthy·Kirthevasan Kandasamy·Barnabas Poczos·Larry Wasserman
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Abstract

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 $\sqrt{n}$-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-Ess\'{e}en style inequality characterizing the rate of convergence to normality. We also show that this estimator is minimax optimal.

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Akshay Krishnamurthy, Kirthevasan Kandasamy, Barnabas Poczos, Larry Wasserman. 2014-10-30. On Estimating $L_2^2$ Divergence. https://arxiv.org/abs/1410.8372

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