Uniform bootstrap central limit theorems for Harris chains

Gabriela Ciolek 1, 2
1 S2A - Signal, Statistique et Apprentissage
LTCI - Laboratoire Traitement et Communication de l'Information
Abstract :

The main objective of this talk 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. We show that in the atomic case the proof of the bootstrap uniform central limit theorem for Markov chains for functions dominated by a function in L2 space proposed by Radulovic (2004) can be significantly simplified. 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. Bertail and Clémençon (2006) have dened an inuence function and Fréchet dierentiability on the torus what allowed to The main objective of this talk 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. We show that in the atomic case the proof of the bootstrap uniform central limit theorem for Markov chains for functions dominated by a function in L2 space proposed by Radulovic (2004) can be signicantly simplified. 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. Bertail and Clémençon (2006) have defined an inluence function and Fréchet differentiability on the torus what allowed to extend the notion of robustness from single observations to the blocks of data instead. In this talk, we present bootstrap uniform central limit theorems for Fréchet differentiable functionals in a Markovian case.The notion of robustness from single observations to the blocks of data instead. In this talk, we present bootstrap uniform central limit theorems for Fréchet differentiable functionals in a Markovian case.

Document type :
Conference papers
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https://hal.telecom-paristech.fr/hal-02287762
Contributor : Telecomparis Hal <>
Submitted on : Friday, September 13, 2019 - 5:19:09 PM
Last modification on : Thursday, October 17, 2019 - 12:37:02 PM

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  • HAL Id : hal-02287762, version 1

Citation

Gabriela Ciolek. Uniform bootstrap central limit theorems for Harris chains. Séminaire de statistique d'AgroParisTech, Jan 2017, Paris, France. ⟨hal-02287762⟩

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