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An empirical Central Limit Theorem in for stationary sequences

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  • Dede, Sophie

Abstract

In this paper, we derive asymptotic results for the -Wasserstein distance between the distribution function and the corresponding empirical distribution function of a stationary sequence. Next, we give some applications to dynamical systems and causal linear processes. To prove our main result, we give a Central Limit Theorem for ergodic stationary sequences of random variables with values in . The conditions obtained are expressed in terms of projective-type conditions. The main tools are martingale approximations.

Suggested Citation

  • Dede, Sophie, 2009. "An empirical Central Limit Theorem in for stationary sequences," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3494-3515, October.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:10:p:3494-3515
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    References listed on IDEAS

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    1. de Araujo, Aloisio Pessoa, 1978. "On the central limit theorem in Banach spaces," Journal of Multivariate Analysis, Elsevier, vol. 8(4), pages 598-613, December.
    2. Volný, Dalibor, 1993. "Approximating martingales and the central limit theorem for strictly stationary processes," Stochastic Processes and their Applications, Elsevier, vol. 44(1), pages 41-74, January.
    3. Dedecker, Jérôme & Doukhan, Paul, 2003. "A new covariance inequality and applications," Stochastic Processes and their Applications, Elsevier, vol. 106(1), pages 63-80, July.
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    Cited by:

    1. Volker Krätschmer & Henryk Zähle, 2017. "Statistical Inference for Expectile-based Risk Measures," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(2), pages 425-454, June.
    2. Lin, Han-Mai & Merlevède, Florence, 2022. "On the weak invariance principle for ortho-martingale in Banach spaces. Application to stationary random fields," Stochastic Processes and their Applications, Elsevier, vol. 153(C), pages 198-220.

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