Laws of Large Numbers and Nearest Neighbor Distances

Mathew D. Penrose () and J. E. Yukich
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Mathew D. Penrose: University of Bath, Department of Mathematical Sciences

Chapter Chapter 13 in Advances in Directional and Linear Statistics, 2011, pp 189-199 from Springer

Abstract: 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.

Keywords: Minimal Span Tree; Tsallis Entropy; Multivariate Density; Unbounded Support; Gaussian Limit (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-7908-2628-9_13

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DOI: 10.1007/978-3-7908-2628-9_13

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