Some peculiar boundary phenomena for extremes of rth nearest neighbor links

H. Dette and N. Henze

Statistics & Probability Letters, 1990, vol. 10, issue 5, 381-390

Abstract: Let Dn,r denote the largest rth nearest neighbor link for n points drawn independently and uniformly from the unit d-cube Cd. We show that according as r d, the limiting behavior of Dn,r, as n --> [infinity], is determined by the two-dimensional 'faces' respectively one-dimensional 'edges' of the boundary of Cd. If d = r, a 'balance' between faces and edges occurs. In case of a d-dimensional sphere (instead of a cube) the boundary dominates the asymptotic behavior of Dn,r if d [greater-or-equal, slanted] 3 or if d = 2, r [greater-or-equal, slanted] 3.

Keywords: Computational; geometry; nearest; neighbor; distances; extreme-value; distribution; boundary; domination; limit; theorem (search for similar items in EconPapers)
Date: 1990
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Citations: View citations in EconPapers (1)

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