IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v122y2012i10p3545-3559.html
   My bibliography  Save this article

Hoeffding’s inequality for supermartingales

Author

Listed:
  • Fan, Xiequan
  • Grama, Ion
  • Liu, Quansheng

Abstract

We give an extension of Hoeffding’s inequality to the case of supermartingales with differences bounded from above. Our inequality strengthens or extends the inequalities of Freedman, Bernstein, Prohorov, Bennett and Nagaev.

Suggested Citation

  • Fan, Xiequan & Grama, Ion & Liu, Quansheng, 2012. "Hoeffding’s inequality for supermartingales," Stochastic Processes and their Applications, Elsevier, vol. 122(10), pages 3545-3559.
    • Handle: RePEc:eee:spapps:v:122:y:2012:i:10:p:3545-3559
    DOI: 10.1016/j.spa.2012.06.009
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414912001378
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2012.06.009?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Lesigne, Emmanuel & Volný, Dalibor, 2001. "Large deviations for martingales," Stochastic Processes and their Applications, Elsevier, vol. 96(1), pages 143-159, November.
    2. Liu, Quansheng & Watbled, Frédérique, 2009. "Exponential inequalities for martingales and asymptotic properties of the free energy of directed polymers in a random environment," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3101-3132, October.
    3. Dzhaparidze, K. & van Zanten, J. H., 2001. "On Bernstein-type inequalities for martingales," Stochastic Processes and their Applications, Elsevier, vol. 93(1), pages 109-117, May.
    4. Grama, Ion & Haeusler, Erich, 2000. "Large deviations for martingales via Cramér's method," Stochastic Processes and their Applications, Elsevier, vol. 85(2), pages 279-293, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Dedecker, Jérôme & Fan, Xiequan, 2015. "Deviation inequalities for separately Lipschitz functionals of iterated random functions," Stochastic Processes and their Applications, Elsevier, vol. 125(1), pages 60-90.
    2. Fan, Xiequan & Alquier, Pierre & Doukhan, Paul, 2022. "Deviation inequalities for stochastic approximation by averaging," Stochastic Processes and their Applications, Elsevier, vol. 152(C), pages 452-485.
    3. Fan, Xiequan, 2017. "Self-normalized deviation inequalities with application to t-statistic," Statistics & Probability Letters, Elsevier, vol. 127(C), pages 158-164.
    4. Rio, Emmanuel, 2017. "New deviation inequalities for martingales with bounded increments," Stochastic Processes and their Applications, Elsevier, vol. 127(5), pages 1637-1648.
    5. Naiqi Liu & Vladimir V. Ulyanov & Hanchao Wang, 2022. "On De la Peña Type Inequalities for Point Processes," Mathematics, MDPI, vol. 10(12), pages 1-13, June.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sason, Igal, 2013. "Tightened exponential bounds for discrete-time conditionally symmetric martingales with bounded jumps," Statistics & Probability Letters, Elsevier, vol. 83(8), pages 1928-1936.
    2. Kanaya, Shin & Otsu, Taisuke, 2012. "Large deviations of realized volatility," Stochastic Processes and their Applications, Elsevier, vol. 122(2), pages 546-581.
    3. Dedecker, Jérôme & Fan, Xiequan, 2015. "Deviation inequalities for separately Lipschitz functionals of iterated random functions," Stochastic Processes and their Applications, Elsevier, vol. 125(1), pages 60-90.
    4. Francis Comets & Nobuo Yoshida, 2011. "Branching Random Walks in Space–Time Random Environment: Survival Probability, Global and Local Growth Rates," Journal of Theoretical Probability, Springer, vol. 24(3), pages 657-687, September.
    5. Kanaya, Shin & Kristensen, Dennis, 2016. "Estimation Of Stochastic Volatility Models By Nonparametric Filtering," Econometric Theory, Cambridge University Press, vol. 32(4), pages 861-916, August.
    6. Fan, Xiequan & Alquier, Pierre & Doukhan, Paul, 2022. "Deviation inequalities for stochastic approximation by averaging," Stochastic Processes and their Applications, Elsevier, vol. 152(C), pages 452-485.
    7. Zhou, Xing-cai & Lin, Jin-guan, 2012. "A wavelet estimator in a nonparametric regression model with repeated measurements under martingale difference error’s structure," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 1914-1922.
    8. Bu, Ruijun & Kim, Jihyun & Wang, Bin, 2023. "Uniform and Lp convergences for nonparametric continuous time regressions with semiparametric applications," Journal of Econometrics, Elsevier, vol. 235(2), pages 1934-1954.
    9. Giraudo, Davide, 2016. "Holderian weak invariance principle under a Hannan type condition," Stochastic Processes and their Applications, Elsevier, vol. 126(1), pages 290-311.
    10. Boucher, Thomas R., 2016. "A note on martingale deviation bounds," Statistics & Probability Letters, Elsevier, vol. 111(C), pages 8-11.
    11. Chen, Qisheng & Zhang, Qian & Liu, Chuan, 2019. "The pricing and numerical analysis of lookback options for mixed fractional Brownian motion," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 123-128.
    12. Emmanuel Rio, 2009. "Moment Inequalities for Sums of Dependent Random Variables under Projective Conditions," Journal of Theoretical Probability, Springer, vol. 22(1), pages 146-163, March.
    13. Anders Bredahl Kock, 2013. "Oracle inequalities for high-dimensional panel data models," CREATES Research Papers 2013-20, Department of Economics and Business Economics, Aarhus University.
    14. Hua-Ming Wang, 2018. "Law of Large Numbers for Random Walk with Unbounded Jumps and Birth and Death Process with Bounded Jumps in Random Environment," Journal of Theoretical Probability, Springer, vol. 31(2), pages 619-642, June.
    15. Stoica, George, 2008. "The Baum-Katz theorem for bounded subsequences," Statistics & Probability Letters, Elsevier, vol. 78(7), pages 924-926, May.
    16. Löcherbach, Eva & Orlandi, Enza, 2011. "Neighborhood radius estimation for variable-neighborhood random fields," Stochastic Processes and their Applications, Elsevier, vol. 121(9), pages 2151-2185, September.
    17. Ruijun Bu & Jihyun Kim & Bin Wang, 2020. "Uniform and Lp Convergences of Nonparametric Estimation for Diffusion Models," Working Papers 202021, University of Liverpool, Department of Economics.
    18. Pepin, Bob, 2021. "Concentration inequalities for additive functionals: A martingale approach," Stochastic Processes and their Applications, Elsevier, vol. 135(C), pages 103-138.
    19. Martin Mbele Bidima & Miklos Rasonyi, 2012. "On long-term arbitrage opportunities in Markovian models of financial markets," Annals of Operations Research, Springer, vol. 200(1), pages 131-146, November.
    20. Fan, Xiequan, 2017. "Self-normalized deviation inequalities with application to t-statistic," Statistics & Probability Letters, Elsevier, vol. 127(C), pages 158-164.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:spapps:v:122:y:2012:i:10:p:3545-3559. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.