Maximal Inequalities for Empirical Processes under General Mixing Conditions
Probability
2026-03-27 v4 Econometrics
Statistics Theory
Statistics Theory
Abstract
This paper provides a bound for the supremum of sample averages over a class of functions for a general class of mixing stochastic processes with arbitrary mixing rates. Regardless of the speed of mixing, the bound is comprised of a concentration rate and a novel measure of complexity. The speed of mixing, however, affects the former quantity implying a phase transition. Fast mixing leads to the standard root-n concentration rate, while slow mixing leads to a slower concentration rate whose speed depends on the mixing structure. Our findings are applied to obtain new Glivenko-Cantelli type results.
Cite
@article{arxiv.2402.11394,
title = {Maximal Inequalities for Empirical Processes under General Mixing Conditions},
author = {Demian Pouzo},
journal= {arXiv preprint arXiv:2402.11394},
year = {2026}
}