Uniform chernoff and dvoretzky-kiefer-wolfowitz-type inequalities for Markov chains and related processes

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13 Scopus citations

Abstract

We observe that the technique of Markov contraction can be used to establish measure concentration for a broad class of noncontracting chains. In particular, geometric ergodicity provides a simple and versatile framework. This leads to a short, elementary proof of a general concentration inequality for Markov and hidden Markov chains, which supersedes some of the knownresults and easily extends to other processes such as Markov trees. As applications, we provide a Dvoretzky-Kiefer-Wolfowitz-type inequality and a uniform Chernoff bound. All of our bounds are dimension-free and hold for countably infinite state spaces.

Original languageEnglish
Pages (from-to)1-14
Number of pages14
JournalJournal of Applied Probability
Volume51
Issue number4
DOIs
StatePublished - 1 Dec 2014

Keywords

  • Chernoff
  • Concentration of measure
  • Dvoretzky-Kiefer-Wolfowitz
  • Hidden Markov chain
  • Markov chain

ASJC Scopus subject areas

  • Statistics and Probability
  • General Mathematics
  • Statistics, Probability and Uncertainty

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