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Maximal inequalities for empirical processes under general mixing conditions

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  • Pouzo, Demian

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.

Suggested Citation

  • Pouzo, Demian, 2026. "Maximal inequalities for empirical processes under general mixing conditions," Stochastic Processes and their Applications, Elsevier, vol. 198(C).
    • Handle: RePEc:eee:spapps:v:198:y:2026:i:c:s0304414926000839
    DOI: 10.1016/j.spa.2026.104951
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