Laws of Large Numbers and Nearest Neighbor Distances
We consider the sum of power weighted nearest neighbor distances in a sample of size n from a multivariate density f of possibly unbounded support. We give various criteria guaranteeing that this sum satisfies a law of large numbers for large n, correcting some inaccuracies in the literature on the way. Motivation comes partly from the problem of consistent estimation of certain entropies of f.
KeywordsMinimal Span Tree Tsallis Entropy Multivariate Density Unbounded Support Gaussian Limit
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Research of Matthew Penrose supported in part by the Alexander von Humboldt Foundation through a Friedrich Wilhelm Bessel Research Award. Research of J.E. Yukich supported in part by NSF grant DMS-0805570.
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