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2011 Asymptotic Moments of Near Neighbor Distances for the Gaussian Distribution
Elia Liitiäinen
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Electron. J. Probab. 16: 2545-2573 (2011). DOI: 10.1214/EJP.v16-969

Abstract

We study the moments of the k-th nearest neighbor distance for independent identically distributed points in $\mathbb{R}^n$. In the earlier literature, the case with power higher than 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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Elia Liitiäinen. "Asymptotic Moments of Near Neighbor Distances for the Gaussian Distribution." Electron. J. Probab. 16 2545 - 2573, 2011. https://doi.org/10.1214/EJP.v16-969

Information

Accepted: 3 December 2011; Published: 2011
First available in Project Euclid: 1 June 2016

zbMATH: 1245.60012
MathSciNet: MR2869415
Digital Object Identifier: 10.1214/EJP.v16-969

Subjects:
Primary: 60D05

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