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A simple variance inequality for U-statistics of a Markov chain with applications

Author

Listed:
  • Fort, G.
  • Moulines, E.
  • Priouret, P.
  • Vandekerkhove, P.

Abstract

We establish a simple variance inequality for U-statistics whose underlying sequence of random variables is an ergodic Markov Chain. The constants in this inequality are explicit and depend on computable bounds on the mixing rate of the Markov Chain. We apply this result to derive the strong law of large numbers for U-statistics of a Markov Chain under conditions which are close to being optimal.

Suggested Citation

  • Fort, G. & Moulines, E. & Priouret, P. & Vandekerkhove, P., 2012. "A simple variance inequality for U-statistics of a Markov chain with applications," Statistics & Probability Letters, Elsevier, vol. 82(6), pages 1193-1201.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:6:p:1193-1201
    DOI: 10.1016/j.spl.2012.02.001
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    References listed on IDEAS

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    1. Harel, Michel & Puri, Madan L., 1990. "Weak invariance of generalized u-statistics for nonstationary absolutely regular processes," Stochastic Processes and their Applications, Elsevier, vol. 34(2), pages 341-360, April.
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    Cited by:

    1. Soukarieh, Inass & Bouzebda, Salim, 2023. "Renewal type bootstrap for increasing degree U-process of a Markov chain," Journal of Multivariate Analysis, Elsevier, vol. 195(C).

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