RATES OF CONVERGENCE FOR RANDOM APPROXIMATIONS OF CONVEX-SETS

Authors
DUMBGEN L WALTHER G
Citation
L. Dumbgen et G. Walther, RATES OF CONVERGENCE FOR RANDOM APPROXIMATIONS OF CONVEX-SETS, Advances in Applied Probability, 28(2), 1996, pp. 384-393
Citations number
7
Categorie Soggetti
Statistic & Probability","Statistic & Probability
Journal title
Advances in Applied Probability → ACNP
ISSN journal
00018678
Volume
28
Issue
2
Year of publication
1996
Pages
384 - 393
Database
ISI
SICI code
0001-8678(1996)28:2<384:ROCFRA>2.0.ZU;2-L
Abstract
The Hausdorff distance between a compact convex set K subset of R(d) a nd random sets (K) over cap subset of R(d) is studied. Basic inequalit ies are derived for the case of (K) over cap being a convex subset of K. If applied to special sequences of such random sets, these inequali ties yield rates of almost sure convergence. With the help of duality considerations these results are extended to the case of (K) over cap being the intersection of a random family of halfspaces containing K.