Asymptotic Moments of Near Neighbor Distances for the Gaussian Distribution

Authors: Elia Liitiäinen

We study the moments E[d1,kα] 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. In the unbounded case, it is shown that E[d1,kα] is asymptotically proportional to M-1 logn-1-α/2M instead of M-α/n as in the previous literature.

Comments: 37 pages, Submitted to a journal

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[v1] 16 May 2011

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