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

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 number for U-statistics of a Markov Chain under conditions which are close from being optimal.
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https://hal.archives-ouvertes.fr/hal-00608574
Contributor : Gersende Fort <>
Submitted on : Wednesday, July 13, 2011 - 2:28:12 PM
Last modification on : Tuesday, December 8, 2020 - 3:41:10 AM
Long-term archiving on: : Friday, October 14, 2011 - 2:40:36 AM

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  • HAL Id : hal-00608574, version 1
  • ARXIV : 1107.2576

Citation

Gersende Fort, Eric Moulines, Pierre Priouret, Pierre Vandekerkhove. A simple variance inequality for U-statistics of a Markov chain with applications. Statistics and Probability Letters, Elsevier, 2012, 82 (6), pp.1193--1201. ⟨hal-00608574⟩

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