{"ID":2852839,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.17648","arxiv_id":"2510.17648","title":"Wild regenerative block bootstrap for Harris recurrent Markov chains","abstract":"We consider Gaussian and bootstrap approximations for the supremum of additive functionals of aperiodic Harris recurrent Markov chains. The supremum is taken over a function class that may depend on the sample size, which allows for non-Donsker settings; that is, the empirical process need not have a weak limit in the space of bounded functions. We first establish a non-asymptotic Gaussian approximation error, which holds at rates comparable to those for sums of high-dimensional independent or one-dependent vectors. Key to our derivation is the Nummelin splitting technique, which enables us to decompose the chain into either independent or one-dependent random blocks. Additionally, building upon the Nummelin splitting, we propose a Gaussian multiplier bootstrap for practical inference and establish its finite-sample guarantees in the strongly aperiodic case. Finally, we apply our bootstrap to construct a uniform confidence band for an invariant density within a certain class of diffusion processes.","short_abstract":"We consider Gaussian and bootstrap approximations for the supremum of additive functionals of aperiodic Harris recurrent Markov chains. The supremum is taken over a function class that may depend on the sample size, which allows for non-Donsker settings; that is, the empirical process need not have a weak limit in the...","url_abs":"https://arxiv.org/abs/2510.17648","url_pdf":"https://arxiv.org/pdf/2510.17648v1","authors":"[\"Kyuseong Choi\",\"Gabriella Ciolek\"]","published":"2025-10-20T15:24:43Z","proceeding":"math.ST","tasks":"[\"math.ST\"]","methods":"[\"Diffusion Model\"]","has_code":false}