Moderate and large deviations for U-processes

被引：3

作者：

Eichelsbacher, P ^{[1
]}

机构：

[1] Univ Bielefeld, Fak Math, D-33501 Bielefeld, Germany

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 1998年 / 74卷 / 02期

关键词：

large deviations; moderate deviations; U-statistics; U-processes; isoperimetric inequality; VC classes; Bernstein's inequality;

D O I：

10.1016/S0304-4149(97)00113-0

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：

Sufficient conditions for the moderate and large deviation principle for U-processes are given. For the large deviation result the conditions are in terms of "blockwise" empirical process conditions. On the moderate scaling the case of U-processes indexed by a uniformly bounded VC subgraph class of functions is considered. The proofs are based on an isoperimetric inequality for empirical processes due to Talagrand, a truncation method based on an isoperimetric inequality by Ledoux, the existence of almost regular partitions of complete hypergraphs due to Baranyai and a Bernstein-type inequality for U-processes due to Arcones and Gine. (C) 1998 Elsevier Science B.V. All rights reserved.

引用

页码：273 / 296

页数：24

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