EXPONENTIAL INEQUALITIES FOR SELF-NORMALIZED MARTINGALES WITH APPLICATIONS

被引：70

作者：

Bercu, Bernard ^{[1
]}

Touati, Abderrahmen ^{[2
]}

机构：

[1] Univ Bordeaux 1, Inst Math Bordeaux, UMR 5251, F-33405 Talence, France

[2] Fac Sci Bizerte, Dept Math, Zarzouna 7021, Tunisia

来源：

ANNALS OF APPLIED PROBABILITY | 2008年 / 18卷 / 05期

关键词：

Exponential inequalities; martingales; autoregressive processes; branching processes;

D O I：

10.1214/07-AAP506

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 propose several exponential inequalities for self-normalized martingales similar to those established by De la Pena. The keystone is the introduction of a new notion of random variable heavy on left or right. Applications associated with linear regressions, autoregressive and branching processes are also provided.

引用

页码：1848 / 1869

页数：22

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