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Exponential inequalities for martingales with applications
- Source :
- Electron. J. Probab. 20 (2015)
- Publication Year :
- 2013
-
Abstract
- 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 Pe\~{n}a, 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 Pe\~{n}a's} inequality to self-normalized deviations is also provided.<br />Comment: 22 pages
- Subjects :
- Mathematics - Probability
60E15, 60G42
Subjects
Details
- Database :
- arXiv
- Journal :
- Electron. J. Probab. 20 (2015)
- Publication Type :
- Report
- Accession number :
- edsarx.1311.6273
- Document Type :
- Working Paper