Statistical Distances Based on Euclidean Graphs

A general approach, based on covering by cells, induced by Euclidean graphs, is developed to provide asymptotic characterizations of multivariate sample densities. This approach provides high dimensional analogs of basic results for random partitions based on one-dimensional sample spacings. The methods used in the proofs yield asymptotics for empirical φ-divergences based on k-spacings and also for the total edge length of the graphs involved.

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