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|
|Editors||Martin T Wells , Ashis SenGupta|
|Place of Publication||Berlin|
|Publication status||Published - 2011|
Penrose, M. D., & Yukich, J. E. (2011). Laws of large numbers and nearest neighbor distances. In M. T. Wells , & A. SenGupta (Eds.), Advances in Directional and Linear Statistics: A Festschrift for Sreenivasa Rao Jammalamadaka (pp. 189-199). Berlin: Physica-Verlag HD . https://doi.org/10.1007/978-3-7908-2628-9_13