Approximate regenerative-block bootstrap for Markov chains: some simulation studies

Patrice Bertail (1, 2) , Stéphan Clémençon (1, 3, 4)

1 MODAL'X - Modélisation aléatoire de Paris X
2 CREST - Centre de Recherche en Économie et Statistique
3 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
4 MET@RISK - Méthodologies d'Analyse de Risque Alimentaire

In [7], a novel methodology for bootstrapping general Harris Markov chains has been developed, the (approximate) regenerative block-bootstrap. It is built on the renewal properties of the chain (or of a Nummelin extension of the latter) and has theoretical properties that surpass other existing methods within the Markovian framework. This paper is devoted to discuss practical issues related to the implementation of this specific resampling method and to present various simulation studies for investigating its performance and comparing it to other bootstrap resampling schemes, standing as natural candidates in the Markov setting.

Domaines: Statistiques [math.ST]

Patrice Bertail, Stéphan Clémençon. Approximate regenerative-block bootstrap for Markov chains: some simulation studies. 2007. ⟨hal-00143105⟩