Laws of large numbers and nearest neighbor distances

Mathew D. Penrose, J. E. Yukich

Published 2009-11-02Version 1

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.