Laws of large numbers and nearest neighbor distances

Details Laws of large numbers and nearest neighbor distances Laws of large numbers and nearest neighbor distances

2009-11-02

arxiv.org/abs/0911.0331v1

Mathematics

Probability

15 pages

Scientific paper

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.

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