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Maximal Inequalities for Empirical Processes under General Mixing Conditions with an Application to Strong Approximations

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  • Demian Pouzo

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, its speed depends on the mixing structure. Our findings are applied to derive strong approximation results for a general class of mixing processes with arbitrary mixing rates.

Suggested Citation

  • Demian Pouzo, 2024. "Maximal Inequalities for Empirical Processes under General Mixing Conditions with an Application to Strong Approximations," Papers 2402.11394, arXiv.org, revised Apr 2024.
    • Handle: RePEc:arx:papers:2402.11394
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    References listed on IDEAS

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    3. Chen, Xiaohong & Hansen, Lars Peter & Carrasco, Marine, 2010. "Nonlinearity and temporal dependence," Journal of Econometrics, Elsevier, vol. 155(2), pages 155-169, April.
    4. Matias D. Cattaneo & Ricardo P. Masini & William G. Underwood, 2022. "Yurinskii's Coupling for Martingales," Papers 2210.00362, arXiv.org, revised Sep 2024.
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