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

G. Fort; E. Moulines; P. Priouret; P. Vandekerkhove

doi:10.1016/j.spl.2012.02.001

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

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

CNRS LTCI
Sorbonne Université
Université Gustave Eiffel

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

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.

langue originale	Anglais
Pages (de - à)	1193-1201
Nombre de pages	9
journal	Statistics and Probability Letters
Volume	82
Numéro de publication	6
Les DOIs	https://doi.org/10.1016/j.spl.2012.02.001
état	Publié - 1 juin 2012
Modification externe	Oui

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10.1016/j.spl.2012.02.001

Contient cette citation

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title = "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 numbers for U-statistics of a Markov Chain under conditions which are close to being optimal.",

keywords = "Inequalities, Law of large numbers, Limit theorems, Markov chains, U-statistics",

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AU - Fort, G.

AU - Moulines, E.

AU - Priouret, P.

AU - Vandekerkhove, P.

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Y1 - 2012/6/1

N2 - 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.

AB - 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.

KW - Inequalities

KW - Law of large numbers

KW - Limit theorems

KW - Markov chains

KW - U-statistics

U2 - 10.1016/j.spl.2012.02.001

DO - 10.1016/j.spl.2012.02.001

M3 - Article

AN - SCOPUS:84859348183

SN - 0167-7152

VL - 82

SP - 1193

EP - 1201

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

IS - 6

ER -

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

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