A boundary corrected expansion of the moments of nearest neighbor distributions

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Journal Title
Journal ISSN
Volume Title
Faculty of Information and Natural Sciences | D4 Julkaistu kehittämis- tai tutkimusraportti taikka -selvitys
Date
2008
Major/Subject
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