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February 2022 Empirical process theory for locally stationary processes
Nathawut Phandoidaen, Stefan Richter
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Bernoulli 28(1): 453-480 (February 2022). DOI: 10.3150/21-BEJ1351

Abstract

We provide a framework for empirical process theory of locally stationary processes using the functional dependence measure. Our results extend known results for stationary Markov chains and mixing sequences by another common possibility to measure dependence and allow for additional time dependence. Our main result is a functional central limit theorem for locally stationary processes. Moreover, maximal inequalities for expectations of sums are developed. We show the applicability of our theory in some examples, for instance, we provide uniform convergence rates for nonparametric regression with locally stationary noise.

Acknowledgements

The authors would like to thank the associate editor and two anonymous referees for their helpful remarks which helped to provide a much more concise version of the paper.

Citation

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Nathawut Phandoidaen. Stefan Richter. "Empirical process theory for locally stationary processes." Bernoulli 28 (1) 453 - 480, February 2022. https://doi.org/10.3150/21-BEJ1351

Information

Received: 1 November 2020; Revised: 1 March 2021; Published: February 2022
First available in Project Euclid: 10 November 2021

Digital Object Identifier: 10.3150/21-BEJ1351

Keywords: Empirical process theory , functional central limit theorem , functional dependence measure , Locally stationary processes , maximal inequality

Rights: Copyright © 2022 ISI/BS

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Vol.28 • No. 1 • February 2022
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