A quantitative McDiarmid's inequality for geometrically ergodic Markov chains

被引：7

作者：

Havet, Antoine ^{[1
]}

Lerasle, Matthieu ^{[2
]}

Moulines, Eric ^{[1
]}

Vernet, Elodie ^{[1
]}

机构：

[1] Ecole Polytech, CMAP, Palaiseau, France

[2] CNRS, CREST, Paris, France

来源：

ELECTRONIC COMMUNICATIONS IN PROBABILITY | 2020年 / 25卷

关键词：

concentration inequalities; Markov chains; geometric ergodicity; coupling;

D O I：

10.1214/20-ECP286

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We state and prove a quantitative version of the bounded difference inequality for geometrically ergodic Markov chains. Our proof uses the same martingale decomposition as [2] but, compared to this paper, the exact coupling argument is modified to fill a gap between the strongly aperiodic case and the general aperiodic case.

引用

页数：11

共 10 条

[1] A tail inequality for suprema of unbounded empirical processes with applications to Markov chains
Adamczak, Radoslaw
[J]. ELECTRONIC JOURNAL OF PROBABILITY, 2008, 13 : 1000 - 1034
[2] Corff S.L., 2018, ARXIV180808104
[3] Subgaussian concentration inequalities for geometrically ergodic Markov chains
Dedecker, Jerome
Gouezel, Sebastien
[J]. ELECTRONIC COMMUNICATIONS IN PROBABILITY, 2015, 20 : 1 - 12
[4] Douc R., 2018, MARKOV CHAINS
[5] Ghosal S, 2017, CA ST PR MA, V44
[6] McDiarmid C., 1989, SURVEYS COMBINATORIC, P148, DOI DOI 10.1017/CBO9781107359949.008
[7] Concentration inequalities for Markov chains by Marton couplings and spectral methods
Paulin, Daniel
[J]. ELECTRONIC JOURNAL OF PROBABILITY, 2015, 20
[8] Roberts G. O., 2004, Probability Surveys, V1, P20, DOI [DOI 10.1214/154957804100000024, 10.1214/154957804100000024]
[9] On the Frequentist Properties of Bayesian Nonparametric Methods
Rousseau, Judith
[J]. ANNUAL REVIEW OF STATISTICS AND ITS APPLICATION, VOL 3, 2016, 3 : 211 - 231
[10] Posterior consistency for nonparametric hidden Markov models with finite state space
Vernet, Elodie
[J]. ELECTRONIC JOURNAL OF STATISTICS, 2015, 9 (01): : 717 - 752

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