Please use this identifier to cite or link to this item: http://scholarbank.nus.edu.sg/handle/10635/103804
Title: On the Hausdorff distance between a convex set and an interior random convex hull
Authors: Bräker, H.
Hsing, T. 
Bingham, N.H.
Keywords: Convex hull
Convex set
Extreme value theory
Gumbel distribution
Hausdorff metric
Home range
Limit law
Moving boundary
Polygon
Smooth boundary
Issue Date: Jun-1998
Source: Bräker, H.,Hsing, T.,Bingham, N.H. (1998-06). On the Hausdorff distance between a convex set and an interior random convex hull. Advances in Applied Probability 30 (2) : 295-316. ScholarBank@NUS Repository.
Abstract: The problem of estimating an unknown compact convex set K in the plane, from a sample (X1, ⋯ , Xn) of points independently and uniformly distributed over K, is considered. Let Knm be the convex hull of the sample, Δ be the Hausdorff distance, and Δn := Δ(K, Kn). Under mild conditions, limit laws for Δn are obtained. We find sequences (an), (bn) such that (Δn - bn)/an → Λ (n → ∞), where Λ is the Gumbel (double-exponential) law from extreme-value theory. As expected, the directions of maximum curvature play a decisive role. Our results apply, for instance, to discs and to the interiors of ellipses, although for eccentricity e < 1 the first case cannot be obtained from the second by continuity. The polygonal case is also considered.
Source Title: Advances in Applied Probability
URI: http://scholarbank.nus.edu.sg/handle/10635/103804
ISSN: 00018678
Appears in Collections:Staff Publications

Show full item record
Files in This Item:
There are no files associated with this item.

Page view(s)

26
checked on Feb 16, 2018

Google ScholarTM

Check


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.