Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-10T15:59:45.214Z Has data issue: false hasContentIssue false
  • English
  • Français

The limit distribution of the largest nearest-neighbour link in the unit d-cube

Published online by Cambridge University Press:  14 July 2016

Holger Dette  and
Norbert Henze
Holger Dette*
Affiliation:
University of Hannover
Norbert Henze*
Affiliation:
University of Hannover
*
∗Postal address: Institut für Mathematische Stochastik, Universität Hannover, Welfengarten 1, D-3000 Hannover 1, W. Germany.
∗Postal address: Institut für Mathematische Stochastik, Universität Hannover, Welfengarten 1, D-3000 Hannover 1, W. Germany.
Get access Rights & Permissions [Opens in a new window]

Abstract

Let·p denote the p-norm on . For n points drawn independently and uniformly from the unit d-cube, we obtain the limit distribution of the largest nearest-neighbour link (with respect to | · |p) in the cases ; (2) d = 3, p = 1, 2, ∞and (3) 4, p =∞.

Keywords

COMPUTATIONAL GEOMETRYNEAREST-NEIGHBOUR DISTANCESEXTREME-VALUE DISTRIBUTIONBOUNDARY DOMINATIONLIMIT THEOREM
Type
Research Papers
Information
Journal of Applied Probability , Volume 26 , Issue 1 , March 1989 , pp. 67 - 80
Copyright
Copyright © Applied Probability Trust 1989 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Galambos, J. (1978) The Asymptotic Theory of Extreme Order Statistics. Wiley, New York.Google Scholar
Henze, N. (1982) The limit distribution for maxima of ‘weighted’ rth-nearest-neighbour distances. J. Appl. Prob. 19, 344–354.Google Scholar
Henze, N. (1983) Ein asymptotischer Satz über den maximalen Minimalabstand von unabhängigen Zufallsvektoren mit Anwendung auf einen Anpassungstest im und auf der Kugel. Metrika 30, 245–259.Google Scholar
Steele, J. M. and Tierney, L. (1986) Boundary domination and the distribution of the largest nearest neighbour link. J. Appl. Prob. 23, 524–528.Google Scholar