A BOUNDARY CORRECTED EXPANSION OF THE MOMENTS OF NEAREST….pdfVIP

TKK Reports in Information and Computer Science Espoo 2008 TKK-ICS-R9 A BOUNDARY CORRECTED EXPANSION OF THE MOMENTS OF NEAREST NEIGHBOR DISTRIBUTIONS Elia Liitia¨inen, Francesco Corona and Amaury Lendasse ABTEKNILLINEN KORKEAKOULU TEKNISKA HÖGSKOLAN HELSINKI UNIVERSITY OF TECHNOLOGY TECHNISCHE UNIVERSITÄT HELSINKI UNIVERSITE DE TECHNOLOGIE D’HELSINKI TKK Reports in Information and Computer Science Espoo 2008 TKK-ICS-R9 A BOUNDARY CORRECTED EXPANSION OF THE MOMENTS OF NEAREST NEIGHBOR DISTRIBUTIONS Elia Liitia¨inen, Francesco Corona and Amaury Lendasse Helsinki University of Technology Faculty of Information and Natural Sciences Department of Information and Computer Science Teknillinen korkeakoulu Informaatio- ja luonnontieteiden tiedekunta Tietojenka¨sittelytieteen laitos Distribution: Helsinki University of Technology Faculty of Information and Natural Sciences Department of Information and Computer Science P.O.Box 5400 FI-02015 TKK FINLAND URL: http://ics.tkk.fi Tel. +358 9 451 1 Fax +358 9 451 3369 E-mail: series@ics.tkk.fi c Elia Liitia¨inen, Francesco Corona and Amaury Lendasse ISBN 978-951-22-9610-1 (Print) ISBN 978-951-22-9611-8 (Online) ISSN 1797-5034 (Print) ISSN 1797-5042 (Online) URL: http://lib.tkk.fi/Reports/2008/isbn9789512296118.pdf TKK ICS Espoo 2008 A BSTRACT: In this paper, the moments of nearest neighbor distance distri- butions 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 result- ing theoretical predictions are tested via simulations and found to be much mo