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Hoeffding's inequality for uniformly ergodic Markov chains

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  • Glynn, Peter W.
  • Ormoneit, Dirk
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    Abstract

    We provide a generalization of Hoeffding's inequality to partial sums that are derived from a uniformly ergodic Markov chain. Our exponential inequality on the deviation of these sums from their expectation is particularly useful in situations where we require uniform control on the constants appearing in the bound.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 56 (2002)
    Issue (Month): 2 (January)
    Pages: 143-146

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    Handle: RePEc:eee:stapro:v:56:y:2002:i:2:p:143-146

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    Keywords: Hoeffding's inequality Markov chains Large deviations;

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    Cited by:
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Ahmad, I.A. & Amezziane, M., 2013. "Probability inequalities for bounded random vectors," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1136-1142.
    6. 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.

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