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Bootstrapping Harris Recurrent Markov Chains

  • Gabriela Ciołek
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 250)

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.

Notes

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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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Gabriela Ciołek
    • 1
  1. 1.LTCI, Télécom ParisTechUniversité Paris-SaclayParisFrance

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