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Bootstrapping Harris Recurrent Markov Chains

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Nonparametric Statistics (ISNPS 2016)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 250))

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Abstract

The main objective of this paper is to present bootstrap uniform functional central limit theorem for Harris recurrent Markov chains over uniformly bounded classes of functions. We show that the result can be generalized also to the unbounded case. To avoid some complicated mixing conditions, we make use of the well-known regeneration properties of Markov chains. Regenerative properties of Markov chains can be applied in order to extend some concepts in robust statistics from i.i.d. to a Markovian setting. It is possible to define an influence function and Fréchet differentiability on the torus which allows to extend the notion of robustness from single observations to the blocks of data instead. We present bootstrap uniform central limit theorems for Fréchet differentiable functionals in a Markovian case.

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Acknowledgements

This work was supported by a public grant as part of the Investissement d’avenir, project reference ANR-11-LABX-0056-LMH.

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Authors and Affiliations

  1. LTCI, Télécom ParisTech, Université Paris-Saclay, Paris, France

    Gabriela Ciołek

Authors
  1. Gabriela Ciołek
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Editors and Affiliations

  1. MODAL’X, Paris West University Nanterre La Défense, Nanterre, France

    Patrice Bertail

  2. LMA, Avignon University, Avignon, France

    Delphine Blanke

  3. MIASHS, University of Rennes 2, Rennes, France

    Pierre-André Cornillon

  4. Formation Continue CEPE, Ecole Nationale de la Statistique et de l’Administration, Malakoff, France

    Eric Matzner-Løber

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Ciołek, G. (2018). Bootstrapping Harris Recurrent Markov Chains. In: Bertail, P., Blanke, D., Cornillon, PA., Matzner-Løber, E. (eds) Nonparametric Statistics. ISNPS 2016. Springer Proceedings in Mathematics & Statistics, vol 250. Springer, Cham. https://doi.org/10.1007/978-3-319-96941-1_25

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