A tail inequality for suprema of unbounded empirical processes with applications to Markov chains

被引：104

作者：

Adamczak, Radoslaw ^{[1
]}

机构：

[1] Polish Acad Sci, Inst Math, PL-00956 Warsaw 10, Poland

来源：

ELECTRONIC JOURNAL OF PROBABILITY | 2008年 / 13卷

关键词：

concentration inequalities; empirical processes; Markov chains;

D O I：

10.1214/EJP.v13-521

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 present a tail inequality for suprema of empirical processes generated by variables with finite psi(alpha) norms and apply it to some geometrically ergodic Markov chains to derive similar estimates for empirical processes of such chains, generated by bounded functions. We also obtain a bounded difference inequality for symmetric statistics of such Markov chains.

引用

页码：1000 / 1034

页数：35

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