Electronic Journal of Statistics

Bootstrap uniform central limit theorems for Harris recurrent Markov chains

Gabriela Ciołek

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Abstract

The main objective of this paper is to establish 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 $L^{2}$ space proposed by Radulović (2004) can be significantly simplified. Finally, we prove bootstrap uniform central limit theorems for Fréchet differentiable functionals in a Markovian setting.

Article information

Source
Electron. J. Statist., Volume 10, Number 2 (2016), 2157-2178.

Dates
First available in Project Euclid: 18 July 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1468849974

Digital Object Identifier
doi:10.1214/16-EJS1167

Mathematical Reviews number (MathSciNet)
MR3522672

Zentralblatt MATH identifier
1347.62063

Subjects
Primary: 62G09: Resampling methods
Secondary: 62G20: Asymptotic properties 60J05: Discrete-time Markov processes on general state spaces

Keywords
Bootstrap Markov chains regenerative processes Nummelin splitting technique empirical processes indexed by classes of functions entropy robustness Fréchet differentiability

Citation

Ciołek, Gabriela. Bootstrap uniform central limit theorems for Harris recurrent Markov chains. Electron. J. Statist. 10 (2016), no. 2, 2157--2178. doi:10.1214/16-EJS1167. https://projecteuclid.org/euclid.ejs/1468849974


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