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