Extremes on Trees

• This paper considers the asymptotic distribution of the longest edge of the minimal spanning tree and nearest neighbor graph on X1,…,XNn where X1,X2,…  are i.i.d. in ℜ2 with distribution F and Nn is independent of the Xi and satisfies Nn/n→p1. A new approach based on spatial blocking and a locally orthogonal coordinate system is developed to treat cases for which F has unbounded support. The general results are applied to a number of special cases, including elliptically contoured distributions, distributions with independent Weibull-like margins and distributions with parallel level curves.

Ämnesord

NATURVETENSKAP  -- Matematik -- Beräkningsmatematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Computational Mathematics (hsv//eng)

Nyckelord

minimal spanning tree

Extreme values

nearest neighbor graph

Extreme values; minimal spanning tree; nearest neighbor graph

Publikations- och innehållstyp

art (ämneskategori)

ref (ämneskategori)