A Bernstein-type inequality for functions of bounded interaction

被引：2
|
作者：
Maurer, Andreas [1 ]
机构：
[1] Adalbertstr 55, D-80799 Munich, Germany
来源：
BERNOULLI | 2019年 / 25卷 / 02期
关键词：
Bernstein inequality; concentration; u-statistics; MOMENT INEQUALITIES; JACKKNIFE ESTIMATE; U-STATISTICS;
D O I：
10.3150/18-BEJ1026
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
We give a distribution-dependent concentration inequality for functions of independent variables. The result extends Bernstein's inequality from sums to more general functions, whose variation in any argument does not depend too much on the other arguments. Applications sharpen existing bounds for U-statistics and the generalization error of regularized least squares.
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页码：1451 / 1471
页数：21
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