Regenerative bootstrap for $\beta$-null recurrent Markov chains
Statistics Theory
2025-09-23 v1 Statistics Theory
Abstract
Two regeneration-based bootstrap methods, namely, the \textit{Regeneration based-bootstrap} \cite{AthreyaFuh1992, Somnat-1993} and the \textit{Regenerative Block bootstrap} \cite{Bertail2006} are shown to be valid for the problem of estimating the integral of a function with respect to the invariant measure in a -null recurrent Markov chain with an accessible atom. An extension of the Central Limit Theorem for randomly indexed sequences is also presented.
Cite
@article{arxiv.2407.05284,
title = {Regenerative bootstrap for $\beta$-null recurrent Markov chains},
author = {Carlos Fernández},
journal= {arXiv preprint arXiv:2407.05284},
year = {2025}
}