On Estimating $L_2^2$ Divergence
Machine Learning
2014-10-31 v1
Abstract
We give a comprehensive theoretical characterization of a nonparametric estimator for the divergence between two continuous distributions. We first bound the rate of convergence of our estimator, showing that it is -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.
Cite
@article{arxiv.1410.8372,
title = {On Estimating $L_2^2$ Divergence},
author = {Akshay Krishnamurthy and Kirthevasan Kandasamy and Barnabas Poczos and Larry Wasserman},
journal= {arXiv preprint arXiv:1410.8372},
year = {2014}
}