On Estimating L22 Divergence
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-Esséen style inequality characterizing the rate of convergence to normality. We also show that this estimator is minimax optimal.
Cite
Text
Krishnamurthy et al. "On Estimating L22 Divergence." International Conference on Artificial Intelligence and Statistics, 2015.Markdown
[Krishnamurthy et al. "On Estimating L22 Divergence." International Conference on Artificial Intelligence and Statistics, 2015.](https://mlanthology.org/aistats/2015/krishnamurthy2015aistats-estimating/)BibTeX
@inproceedings{krishnamurthy2015aistats-estimating,
title = {{On Estimating L22 Divergence}},
author = {Krishnamurthy, Akshay and Kandasamy, Kirthevasan and Póczos, Barnabás and Wasserman, Larry A.},
booktitle = {International Conference on Artificial Intelligence and Statistics},
year = {2015},
url = {https://mlanthology.org/aistats/2015/krishnamurthy2015aistats-estimating/}
}