Asymptotically Unbiased Estimator of the Informational Energy with kNN
Keywords:machine learning, statistical inference, asymptotically unbiased estimator, k-th nearest neighbor, informational energy
Motivated by machine learning applications (e.g., classification, functionÂ approximation, feature extraction), in previous work, we have introduced a nonparametricÂ estimator of Onicescu’s informational energy. Our method was based onÂ the k-th nearest neighbor distances between the n sample points, where k is a fixedÂ positive integer. In the present contribution, we discuss mathematical properties ofÂ this estimator. We show that our estimator is asymptotically unbiased and consistent.Â We provide further experimental results which illustrate the convergence of theÂ estimator for standard distributions.
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