Rates of convergence for random approximations of convex sets
Rates of convergence for random approximations of convex sets
复制标题
凸集随机近似的收敛率
DOI：
10.2307/1428063
复制
发表时间：
1996
影响因子：
1.2
通讯作者：
Gunther Walther
中科院分区：
文献类型：
--
作者：
L. Dümbgen;Gunther Walther
研究了紧凸集K∧∈d与随机集之间的豪斯多夫距离。对于k的一个凸子集，导出了基本不等式。如果将这些不等式应用于这种随机集的特殊序列，则这些不等式的收敛率几乎是肯定的。借助对偶考虑，将这些结果推广到含有K的随机半空间族的交点的情况。
The Hausdorff distance between a compact convex set K ⊂ ℝd and random sets is studied. Basic inequalities are derived for the case of being a convex subset of K. If applied to special sequences of such random sets, these inequalities yield rates of almost sure convergence. With the help of duality considerations these results are extended to the case of being the intersection of a random family of halfspaces containing K.