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.
|Title of host publication
|Advances in Directional and Linear Statistics:
|Subtitle of host publication
|A Festschrift for Sreenivasa Rao Jammalamadaka
|Martin T Wells , Ashis SenGupta
|Place of Publication
|Published - 2011