Maximal Inequalities for Empirical Processes under General Mixing Conditions

Demian Pouzo

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arXiv · 2402.11394

Maximal Inequalities for Empirical Processes under General Mixing Conditions

Demian Pouzo

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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.

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Demian Pouzo. 2024-02-17. Maximal Inequalities for Empirical Processes under General Mixing Conditions. https://arxiv.org/abs/2402.11394

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