A boundary corrected expansion of the moments of nearest neighbor distributions

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dc.contributor Aalto-yliopisto fi
dc.contributor Aalto University en
dc.contributor.author Liitiäinen, Elia
dc.contributor.author Corona, Francesco
dc.contributor.author Lendasse, Amaury
dc.date.accessioned 2011-11-28T13:19:34Z
dc.date.available 2011-11-28T13:19:34Z
dc.date.issued 2008
dc.identifier.isbn 978-951-22-9611-8
dc.identifier.issn 1797-5042
dc.identifier.uri https://aaltodoc.aalto.fi/handle/123456789/882
dc.description.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. en
dc.format.extent 29
dc.format.mimetype application/pdf
dc.language.iso en en
dc.publisher Helsinki University of Technology en
dc.publisher Teknillinen korkeakoulu fi
dc.relation.ispartofseries TKK reports in information and computer science en
dc.relation.ispartofseries 9 en
dc.subject.other Computer science en
dc.title A boundary corrected expansion of the moments of nearest neighbor distributions en
dc.type D4 Julkaistu kehittämis- tai tutkimusraportti taikka -selvitys fi
dc.contributor.school Faculty of Information and Natural Sciences en
dc.contributor.school Informaatio- ja luonnontieteiden tiedekunta fi
dc.contributor.department Department of Information and Computer Science en
dc.contributor.department Tietojenkäsittelytieteen laitos fi
dc.subject.keyword nearest neighbor en
dc.subject.keyword boundary en
dc.subject.keyword asymptotics en
dc.subject.keyword Renyi entropy en
dc.identifier.urn urn:nbn:fi:tkk-012328
dc.type.dcmitype text en

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