A boundary corrected expansion of the moments of nearest neighbor distributions

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Volume Title

Faculty of Information and Natural Sciences | D4 Julkaistu kehittämis- tai tutkimusraportti taikka -selvitys

Date

2008

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Mcode

Degree programme

Language

en

Pages

29

Series

TKK reports in information and computer science, 9

Abstract

In this paper, the moments of nearest neighbor distance distributions are examined. While the asymptotic form of such moments is well-known, the boundary effect has this far resisted a rigorous analysis. Our goal is to develop a new technique that allows a closed-form high order expansion, where the boundaries are taken into account up to the first order. The resulting theoretical predictions are tested via simulations and found to be much more accurate than the first order approximation obtained by neglecting the boundaries. While our results are of theoretical interest, they definitely also have important applications in statistics and physics. As a concrete example, we mention estimating Renyi entropies of probability distributions. Moreover, the algebraic technique developed may turn out to be useful in other, related problems including estimation of the Shannon differential entropy.

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Keywords

nearest neighbor, boundary, asymptotics, Renyi entropy

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Permanent link to this item

https://urn.fi/urn:nbn:fi:tkk-012328