Renewal Type Bootstrap for Markov Chains

• Autores: Dragan Radulovic
• Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 13, Nº. 1, 2004, págs. 147-192
• Idioma: inglés
• DOI: 10.1007/bf02603005
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• Resumen

  • In this paper we treat a renewal type of bootstrap for atomic Markov chains under minimal moment conditions on renewal times, i.e. E\tau ^{2}<\infty. 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 function $F;$ c) we establish second order correctness for this procedure. All results are for "in probability" bootstrap and constitute the final word in this setting.