Exponential inequalities for martingales with applications
Exponential inequalities for martingales with applications
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DOI：
10.1214/ejp.v20-3496
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发表时间：
2013-11
影响因子：
1.4
通讯作者：
Xiequan Fan;Ion Grama;Quansheng Liu
中科院分区：
文献类型：
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作者：
Xiequan Fan;Ion Grama;Quansheng Liu
本文致力于建立超鞅的一些一般指数不等式。这些不等式改进或概括了贝内特、弗里德曼、德拉佩纳、皮内利斯和范德吉尔的许多指数不等式。此外，我们的集中不等式还改进了一些已知的独立随机变量之和的不等式。提供了与线性回归、自回归过程和分支过程相关的应用程序。特别是，还提供了德拉佩纳不等式在自我归一化偏差中的有趣应用。
The paper is devoted to establishing some general exponential inequalities for supermartingales. The inequalities improve or generalize many exponential inequalities of Bennett, Freedman, de la Pena, Pinelis and van de Geer. Moreover, our concentration inequalities also improve some known inequalities for sums of independent random variables. Applications associated with linear regressions, autoregressive processes and branching processes are provided. In particular, an interesting application of de la Pena’s inequality to self-normalized deviations is also provided.