2014/10/30 by Krishnamurthy, Akshay, Kandasamy, Kirthevasan, Poczos, Barnabas +1
#FOS: Computer and information sciences #Machine Learning (stat.ML)
paper · doi:10.48550/arxiv.1410.8372
We give a comprehensive theoretical characterization of a nonparametric estimator for the L22 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.