IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v200y2023ics0167715223000949.html
   My bibliography  Save this article

Hoeffding’s inequality for non-irreducible Markov models

Author

Listed:
  • Sandrić, Nikola
  • Šebek, Stjepan

Abstract

In this article, we establish Hoeffding’s inequality for bounded Lipschitz functions of a class of not necessarily irreducible Markov models. The result complements the existing literature on this topic where Hoeffding’s inequality for bounded measurable functions of a class of irreducible Markov models has been considered. Our approach is based on the assumption of uniform ergodicity of the underlying Markov model in L1-Wasserstein space.

Suggested Citation

  • Sandrić, Nikola & Šebek, Stjepan, 2023. "Hoeffding’s inequality for non-irreducible Markov models," Statistics & Probability Letters, Elsevier, vol. 200(C).
    • Handle: RePEc:eee:stapro:v:200:y:2023:i:c:s0167715223000949
    DOI: 10.1016/j.spl.2023.109870
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715223000949
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2023.109870?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. Choi, Michael C.H. & Li, Evelyn, 2019. "A Hoeffding’s inequality for uniformly ergodic diffusion process," Statistics & Probability Letters, Elsevier, vol. 150(C), pages 23-28.
    2. Yongqiang Tang, 2007. "A Hoeffding-Type Inequality for Ergodic Time Series," Journal of Theoretical Probability, Springer, vol. 20(2), pages 167-176, June.
    3. Glynn, Peter W. & Ormoneit, Dirk, 2002. "Hoeffding's inequality for uniformly ergodic Markov chains," Statistics & Probability Letters, Elsevier, vol. 56(2), pages 143-146, January.
    4. Boucher, Thomas R., 2009. "A Hoeffding inequality for Markov chains using a generalized inverse," Statistics & Probability Letters, Elsevier, vol. 79(8), pages 1105-1107, April.
    5. Miasojedow, Błażej, 2014. "Hoeffding’s inequalities for geometrically ergodic Markov chains on general state space," Statistics & Probability Letters, Elsevier, vol. 87(C), pages 115-120.
    Full references (including those not matched with items on IDEAS)

    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. Liu, Jinpeng & Liu, Yuanyuan & Zhao, Yiqiang Q., 2022. "Augmented truncation approximations to the solution of Poisson’s equation for Markov chains," Applied Mathematics and Computation, Elsevier, vol. 414(C).
    2. Ahmad, I.A. & Amezziane, M., 2013. "Probability inequalities for bounded random vectors," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1136-1142.
    3. Choi, Michael C.H. & Li, Evelyn, 2019. "A Hoeffding’s inequality for uniformly ergodic diffusion process," Statistics & Probability Letters, Elsevier, vol. 150(C), pages 23-28.
    4. H. S. Chang, 2004. "Technical Note: On Ordinal Comparison of Policies in Markov Reward Processes," Journal of Optimization Theory and Applications, Springer, vol. 122(1), pages 207-217, July.
    5. Yongqiang Tang, 2007. "A Hoeffding-Type Inequality for Ergodic Time Series," Journal of Theoretical Probability, Springer, vol. 20(2), pages 167-176, June.
    6. Fan, Jianqing & Guo, Yongyi & Jiang, Bai, 2022. "Adaptive Huber regression on Markov-dependent data," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 802-818.
    7. Shie Mannor & John N. Tsitsiklis, 2005. "On the Empirical State-Action Frequencies in Markov Decision Processes Under General Policies," Mathematics of Operations Research, INFORMS, vol. 30(3), pages 545-561, August.
    8. Miasojedow, Błażej, 2014. "Hoeffding’s inequalities for geometrically ergodic Markov chains on general state space," Statistics & Probability Letters, Elsevier, vol. 87(C), pages 115-120.
    9. Renou, Ludovic & Tomala, Tristan, 2015. "Approximate implementation in Markovian environments," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 401-442.
    10. Koch, Erwan & Robert, Christian Y., 2019. "Geometric ergodicity for some space–time max-stable Markov chains," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 43-49.
    11. Penev, Spiridon & Peng, Hanxiang & Schick, Anton & Wefelmeyer, Wolfgang, 2004. "Efficient estimators for functionals of Markov chains with parametric marginals," Statistics & Probability Letters, Elsevier, vol. 66(3), pages 335-345, February.
    12. Hunt, F.Y., 2005. "Sample path optimality for a Markov optimization problem," Stochastic Processes and their Applications, Elsevier, vol. 115(5), pages 769-779, May.
    13. Ankush Agarwal & Stefano de Marco & Emmanuel Gobet & Gang Liu, 2017. "Rare event simulation related to financial risks: efficient estimation and sensitivity analysis," Working Papers hal-01219616, HAL.
    14. Svetlana Ekisheva & Mark Borodovsky, 2011. "Uniform Accuracy of the Maximum Likelihood Estimates for Probabilistic Models of Biological Sequences," Methodology and Computing in Applied Probability, Springer, vol. 13(1), pages 105-120, March.
    15. Boucher, Thomas R., 2009. "A Hoeffding inequality for Markov chains using a generalized inverse," Statistics & Probability Letters, Elsevier, vol. 79(8), pages 1105-1107, April.
    16. Lember, Jüri & Matzinger, Heinrich & Sova, Joonas & Zucca, Fabio, 2018. "Lower bounds for moments of global scores of pairwise Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 128(5), pages 1678-1710.
    17. Chang, Hyeong Soo, 2006. "On convergence rate of the Shannon entropy rate of ergodic Markov chains via sample-path simulation," Statistics & Probability Letters, Elsevier, vol. 76(12), pages 1261-1264, July.

    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:stapro:v:200:y:2023:i:c:s0167715223000949. 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/622892/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.