Exponential inequalities for martingales with applications
By Xiequan Fan, Ion Grama, Quansheng Liu. 2013
115 citations recorded by the source corpus.
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.
Subfields: Artificial Intelligence, Management Science and Operations Research, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/d3ab9345af39da8e10069ff6c5aed2a6f274dda5
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In Artificial Intelligence
- Aaditya Ramdas
- Ian Waudby-Smith
- Jon D. McAuliffe
- Steven R. Howard
- Jasjeet S. Sekhon
- David M. Blei
- Michael I. Jordan
- Francis R. Bach
In Management Science and Operations Research
In Mathematical Physics
Citations in the corpus
- Time-uniform Chernoff bounds via nonnegative supermartingales (2018, methodology): “This “Freedman-style” bound has been generalized to other settings in many subsequent works (de la Peña, 1999; Khan, 2009; Tropp, 2011; Fan et al., 2015).”
- Uniform, nonparametric, non-asymptotic confidence sequences (2018, background): “The proof of Lemma 4.1 in Fan et al. (2015) shows that exp { λξ − ψE(λ)ξ2 } ≤ 1 + λξ for all λ ∈ [0, 1) and ξ ≥ −1.”
- Estimating means of bounded random variables by betting (2020, background): “[39] along with an additional trick which permits the use of a predictable μ̂t−1 in the place of μ [1, Section A.”