Asymptotic moments of near neighbor distances for the gaussian distribution

Elia Liitiäinen

Asymptotic moments of near neighbor distances for the gaussian distribution

Elia Liitiäinen^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › Scientific › peer-review

2 Citations (Scopus)

Abstract

We study the moments E[d^α _1,k] of the k-th nearest neighbor distance for independent identically distributed points in Rⁿ. In the earlier literature, the case α > n has been analyzed by assuming a bounded support for the underlying density. The boundedness assumption is removed by assuming the multivariate Gaussian distribution. In this case, the nearest neighbor distances show very different behavior in comparison to earlier results.

Original language	English
Pages (from-to)	2545-2573
Number of pages	29
Journal	Electronic Journal of Probability
Volume	16
Publication status	Published - 2011
MoE publication type	A1 Journal article-refereed

Keywords

Gaussian
Moments
Nearest neighbor
Random geometry

Cite this

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abstract = "We study the moments E[dα 1,k] of the k-th nearest neighbor distance for independent identically distributed points in Rn. In the earlier literature, the case α > n has been analyzed by assuming a bounded support for the underlying density. The boundedness assumption is removed by assuming the multivariate Gaussian distribution. In this case, the nearest neighbor distances show very different behavior in comparison to earlier results.",

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AU - Liitiäinen, Elia

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AB - We study the moments E[dα 1,k] of the k-th nearest neighbor distance for independent identically distributed points in Rn. In the earlier literature, the case α > n has been analyzed by assuming a bounded support for the underlying density. The boundedness assumption is removed by assuming the multivariate Gaussian distribution. In this case, the nearest neighbor distances show very different behavior in comparison to earlier results.

KW - Gaussian

KW - Moments

KW - Nearest neighbor

KW - Random geometry

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M3 - Article

AN - SCOPUS:83255181635

SN - 1083-6489

VL - 16

SP - 2545

EP - 2573

JO - Electronic Journal of Probability

JF - Electronic Journal of Probability

ER -

Asymptotic moments of near neighbor distances for the gaussian distribution

Abstract

Keywords

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