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Regenerative block empirical likelihood for Markov chains

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  • Hugo Harari-Kermadec

Abstract

Empirical likelihood (EL) is a powerful semi-parametric method increasingly investigated in the literature. However, most authors essentially focus on an i.i.d. setting. In the case of dependent data, the classical EL method cannot be directly applied on the data but rather on blocks of consecutive data catching the dependence structure. Generalisation of EL based on the construction of blocks of increasing random length have been proposed for time series satisfying mixing conditions. Following some recent developments in the bootstrap literature, we propose a generalisation for a large class of Markov chains, based on small blocks of various lengths. Our approach makes use of the regenerative structure of Markov chains, which allows us to construct blocks which are almost independent (independent in the atomic case). We obtain the asymptotic validity of the method for positive recurrent Markov chains and present some simulation results.

Suggested Citation

  • Hugo Harari-Kermadec, 2011. "Regenerative block empirical likelihood for Markov chains," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(3), pages 781-802.
  • Handle: RePEc:taf:gnstxx:v:23:y:2011:i:3:p:781-802
    DOI: 10.1080/10485252.2011.565340
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    References listed on IDEAS

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    1. Paul Doukhan & Patrice Bertail & Philippe Soulier, 2006. "Dependence in Probability and Statistics," Post-Print hal-00268232, HAL.
    2. Paul Doukhan & Patrice Bertail & Philippe Soulier, 2006. "Dependence in Probability and Statistics," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00268232, HAL.
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