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A large deviation inequality for β-mixing time series and its applications to the functional kernel regression model

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  • Krebs, Johannes T.N.

Abstract

We give a new large deviation inequality for sums of random variables of the form Zk=f(Xk,Xt) for k,t∈N, t fixed, where the underlying process X is β-mixing. The inequality can be used to derive concentration inequalities. We demonstrate its usefulness in the functional kernel regression model of Ferraty et al. (2007) where we study the consistency of dynamic forecasts.

Suggested Citation

  • Krebs, Johannes T.N., 2018. "A large deviation inequality for β-mixing time series and its applications to the functional kernel regression model," Statistics & Probability Letters, Elsevier, vol. 133(C), pages 50-58.
    • Handle: RePEc:eee:stapro:v:133:y:2018:i:c:p:50-58
    DOI: 10.1016/j.spl.2017.09.013
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    References listed on IDEAS

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    1. Ahmad, I.A. & Amezziane, M., 2013. "Probability inequalities for bounded random vectors," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1136-1142.
    2. Frédéric Ferraty & Ingrid Van Keilegom & Philippe Vieu, 2010. "On the Validity of the Bootstrap in Non‐Parametric Functional Regression," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(2), pages 286-306, June.
    3. Arcones, Miguel A., 1995. "A Bernstein-type inequality for U-statistics and U-processes," Statistics & Probability Letters, Elsevier, vol. 22(3), pages 239-247, February.
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