A Bennett concentration inequality and its application to suprema of empirical processes

被引：146

作者：

Bousquet, O ^{[1
]}

机构：

[1] Ecole Polytech, CMAP, F-91128 Palaiseau, France

来源：

COMPTES RENDUS MATHEMATIQUE | 2002年 / 334卷 / 06期

关键词：

D O I：

10.1016/S1631-073X(02)02292-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We introduce new concentration inequalities for functions on product spaces. They allow to obtain a Bennett type deviation bound for suprema of empirical processes indexed by upper bounded functions. The result is an improvement on Rio's version [6] of Talagrand's inequality [7] for equidistributed variables.

引用

页码：495 / 500

页数：6

共 8 条

[1] Boucheron S, 2000, RANDOM STRUCT ALGOR, V16, P277, DOI 10.1002/(SICI)1098-2418(200005)16:3<277::AID-RSA4>3.0.CO
[2] 2-1
[3] BOUCHERON S, 2001, UNPUB CONCENTRATION
[4] Ledoux M., 1995, ESAIM Probab. Statist., V1, P63
[5] About the constants in Talagrand's concentration inequalities for empirical processes
Massart, P
[J]. ANNALS OF PROBABILITY, 2000, 28 (02) : 863 - 884
[6] Rio E, 2001, PROBAB THEORY REL, V119, P163, DOI 10.1007/PL00008756
[7] RIO E, 2001, IN PRESS C HONNEUR J
[8] New concentration inequalities in product spaces
Talagrand, M
[J]. INVENTIONES MATHEMATICAE, 1996, 126 (03) : 505 - 563

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