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

G. Fort, E. Moulines, P. Priouret and P. Vandekerkhove

Statistics & Probability Letters, 2012, vol. 82, issue 6, 1193-1201

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.

Keywords: U-statistics; Markov chains; Inequalities; Limit theorems; Law of large numbers (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spl.2012.02.001

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