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Probability inequalities for bounded random vectors

Author

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  • Ahmad, I.A.
  • Amezziane, M.

Abstract

Probability inequalities are powerful tools that can be applied in many areas such as laws of large numbers, central limit theorem, law of iterated logarithm, deviation probabilities and asymptotics of inference problems. In this work, extensions of the basic inequalities of Bernstein, Kolmogorov and Hoeffding are given for the sums of bounded random vectors.

Suggested Citation

  • Ahmad, I.A. & Amezziane, M., 2013. "Probability inequalities for bounded random vectors," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1136-1142.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:4:p:1136-1142
    DOI: 10.1016/j.spl.2012.11.023
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
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    Cited by:

    1. Krebs, Johannes T.N., 2018. "A large deviation inequality for β-mixing time series and its applications to the functional kernel regression model," Statistics & Probability Letters, Elsevier, vol. 133(C), pages 50-58.
    2. Minsker, Stanislav, 2017. "On some extensions of Bernstein’s inequality for self-adjoint operators," Statistics & Probability Letters, Elsevier, vol. 127(C), pages 111-119.

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