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Dependence Modeling

Ed. by Puccetti, Giovanni


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CiteScore 2018: 0.67

SCImago Journal Rank (SJR) 2018: 0.380
Source Normalized Impact per Paper (SNIP) 2018: 0.383

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2300-2298
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Exponential inequalities for nonstationary Markov chains

Pierre Alquier / Paul Doukhan / Xiequan Fan
Published Online: 2019-06-03 | DOI: https://doi.org/10.1515/demo-2019-0007

Abstract

Exponential inequalities are main tools in machine learning theory. To prove exponential inequalities for non i.i.d random variables allows to extend many learning techniques to these variables. Indeed, much work has been done both on inequalities and learning theory for time series, in the past 15 years. However, for the non independent case, almost all the results concern stationary time series. This excludes many important applications: for example any series with a periodic behaviour is nonstationary. In this paper, we extend the basic tools of [19] to nonstationary Markov chains. As an application, we provide a Bernsteintype inequality, and we deduce risk bounds for the prediction of periodic autoregressive processes with an unknown period.

Keywords: Nonstationary Markov chains; Martingales; Exponential inequalities; Time series forecasting; Statistical learning theory; Oracle inequalities; Model selection

MSC 2010: 60J05; 60E15; 62M20; 62M05; 62M10; 68Q32

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About the article

Received: 2019-01-18

Accepted: 2019-05-04

Published Online: 2019-06-03

Published in Print: 2019-01-01


Citation Information: Dependence Modeling, Volume 7, Issue 1, Pages 150–168, ISSN (Online) 2300-2298, DOI: https://doi.org/10.1515/demo-2019-0007.

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© 2019 Pierre Alquier et al., published by De Gruyter. This work is licensed under the Creative Commons Attribution 4.0 Public License. BY 4.0

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