Laws of Large Numbers and Nearest Neighbor Distances

  • Mathew D. Penrose
  • J. E. Yukich


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.


Minimal Span Tree Tsallis Entropy Multivariate Density Unbounded Support Gaussian Limit 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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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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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Department of Mathematical SciencesUniversity of BathBathUK

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