Abstract
Two regeneration-based bootstrap methods, namely, the Regeneration based-bootstrap [3, 23] and the Regenerative Block bootstrap [11] are shown to be valid for the problem of estimating the integral of a function with respect to the invariant measure in a β-null recurrent Markov chain with an accessible atom. An extension of the Central Limit Theorem for randomly indexed sequences is also presented.
Funding Statement
This research has been conducted as part of the project Labex MME-DII (ANR11-LBX-0023-01) and has also been funded by a post doctoral grant of the Hi! Paris foundation.
Acknowledgments
The author would like to thank the two anonymous referees and the Associate Editor for their constructive comments that greatly improved the quality of this paper. A significant part of this work was conducted during the author’s PhD at Université Pars-Nanterre.
Citation
Carlos A. Fernández. "Regenerative bootstrap for β-null recurrent Markov chains." Electron. J. Statist. 18 (2) 4851 - 4881, 2024. https://doi.org/10.1214/24-EJS2318
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