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, Volume 13, Issue 1, pp 147–192 | Cite as

Renewal type bootstrap for Markov chains

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Abstract

In this paper we treat a renewal type of bootstrap for atomic Markov chains under minimal moment conditions on renewal times, i.e.Er 2<∞. Three main results are: a) if a Markov chain satisfies the CLT for the mean then it also satisfies a bootstrap CLT; b) if a Markov chain satisfies a uniform CLT over classes of functions then, it also satisfies bootstrap uniform CLT with minimal condition on envelope functionF; c) we establish second order correctness for this procedure. All results are for “in probability” bootstrap and constitute the final word in this setting.

Key Words

Markov chains Bootstrap Empirical processes 

AMS subject classification

62F03 62A05 
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Copyright information

© Sociedad Española de Estadística e Investigación Operativa 2004

Authors and Affiliations

  1. 1.Department of MathematicsFlorida Atlantic UniversityBoca RatonU.S.A.

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