{"id":606708,"date":"2019-09-02T14:21:34","date_gmt":"2019-09-02T21:21:34","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/?post_type=msr-research-item&p=606708"},"modified":"2020-08-28T16:57:55","modified_gmt":"2020-08-28T23:57:55","slug":"on-estimating-l_22-divergence","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/on-estimating-l_22-divergence\/","title":{"rendered":"On Estimating L_2^2 Divergence"},"content":{"rendered":"

We give a comprehensive theoretical characterization of a nonparametric estimator for the \\(L_2^2\\)<\/span><\/span><\/span><\/span><\/span> divergence between two continuous distributions. We first bound the rate of convergence of our estimator, showing that it is \\(\\)\\sqrt{<\/span><\/span><\/span><\/span><\/span>n}[\\latex]<\/span><\/span><\/span><\/span><\/span><\/span>-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\u00e9en style inequality characterizing the rate of convergence to normality. We also show that this estimator is minimax optimal.<\/p>\n","protected":false},"excerpt":{"rendered":"

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 \\sqrt{n}[\\latex]-consistent provided the densities are sufficiently smooth. In this smooth regime, we then show that our estimator is asymptotically normal, construct asymptotic confidence intervals, 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