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An empirical central limit theorem for dependent sequences

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  • Dedecker, Jérôme
  • Prieur, Clémentine

Abstract

We prove a central limit theorem for the d-dimensional distribution function of a class of stationary sequences. The conditions are expressed in terms of some coefficients which measure the dependence between a given [sigma]-algebra and indicators of quadrants. These coefficients are weaker than the corresponding mixing coefficients, and can be computed in many situations. In particular, we show that they are well adapted to functions of mixing sequences, iterated random functions, and a class of dynamical systems.

Suggested Citation

  • Dedecker, Jérôme & Prieur, Clémentine, 2007. "An empirical central limit theorem for dependent sequences," Stochastic Processes and their Applications, Elsevier, vol. 117(1), pages 121-142, January.
    • Handle: RePEc:eee:spapps:v:117:y:2007:i:1:p:121-142
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    References listed on IDEAS

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    1. Doukhan, Paul & Louhichi, Sana, 1999. "A new weak dependence condition and applications to moment inequalities," Stochastic Processes and their Applications, Elsevier, vol. 84(2), pages 313-342, December.
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    Cited by:

    1. Gourieroux, Christian & Jasiak, Joann, 2019. "Robust analysis of the martingale hypothesis," Econometrics and Statistics, Elsevier, vol. 9(C), pages 17-41.
    2. Dehling, Herold & Durieu, Olivier, 2011. "Empirical processes of multidimensional systems with multiple mixing properties," Stochastic Processes and their Applications, Elsevier, vol. 121(5), pages 1076-1096, May.
    3. Olivier Durieu & Marco Tusche, 2014. "An Empirical Process Central Limit Theorem for Multidimensional Dependent Data," Journal of Theoretical Probability, Springer, vol. 27(1), pages 249-277, March.
    4. Dehling, Herold & Durieu, Olivier & Volny, Dalibor, 2009. "New techniques for empirical processes of dependent data," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3699-3718, October.
    5. Berkes, István & Hörmann, Siegfried & Schauer, Johannes, 2009. "Asymptotic results for the empirical process of stationary sequences," Stochastic Processes and their Applications, Elsevier, vol. 119(4), pages 1298-1324, April.
    6. Christophe Cuny & Florence Merlevède, 2015. "Strong Invariance Principles with Rate for “Reverse” Martingale Differences and Applications," Journal of Theoretical Probability, Springer, vol. 28(1), pages 137-183, March.

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