论文标题
不完整的U统计量的指数有限样本边界
Exponential finite sample bounds for incomplete U-statistics
论文作者
论文摘要
已经提出了不完整的U统计量来加速计算。他们仅使用通过完整的U统计量使用内核评估所需的子样本子集。本文以伯恩斯坦不平等的风格提供了有限的样本。应用于完成U统计量，导致的不平等在Hoeffding和Arcones的边界上都提高了。对于随机确定的子样本，显示出，一旦其数字达到样本大小的平方，就可以获得与完整统计量相同的顺序结合。
Incomplete U-statistics have been proposed to accelerate computation. They use only a subset of the subsamples required for kernel evaluations by complete U-statistics. This paper gives a finite sample bound in the style of Bernstein's inequality. Applied to complete U-statistics the resulting inequality improves over the bounds of both Hoeffding and Arcones. For randomly determined subsamples it is shown, that, as soon as the their number reaches the square of the sample-size, the same order bound is obtained as for the complete statistic.
