Approximate regenerative-block bootstrap for Markov chains

Authors:
Patrice Bertail;Stéphan Clémençon
Affiliations:
Laboratoire de Statistique, CREST, INSEE, France and MODALX, Université Paris X, 200 av. de la République, 92000 Nanterre Cedex, France;MODALX, Université Paris X, 200 av. de la République, 92000 Nanterre Cedex, France and Unité Metarisk, Institut National de le Recherche Agronomique, France and LPMA, UMR CNRS 7599, ...
Venue:
Computational Statistics & Data Analysis
Year:
2008

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Abstract

The (approximate) regenerative block-bootstrap for bootstrapping general Harris Markov chains has recently been developed. It is built on the renewal properties of the chain, or of a Nummelin extension of the latter. It has theoretical properties that surpass other existing methods within the Markovian framework. The practical issues related to the implementation of this specific resampling method are discussed. Various simulation studies for investigating its performance and comparing it to other bootstrap resampling schemes, standing as natural candidates in the Markov setting are presented.