Laws of large numbers and nearest neighbor distances

M D Penrose, J E Yukich

Research output: Chapter in Book/Report/Conference proceedingChapter

10 Citations (Scopus)

Abstract

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.
Original languageEnglish
Title of host publicationAdvances in Directional and Linear Statistics:
Subtitle of host publicationA Festschrift for Sreenivasa Rao Jammalamadaka
EditorsMartin T Wells , Ashis SenGupta
Place of PublicationBerlin
PublisherPhysica-Verlag HD
Pages189-199
ISBN (Electronic)9783790826289
ISBN (Print)9783790826272
DOIs
Publication statusPublished - 2011

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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