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Asymptotic results for the empirical process of stationary sequences

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  • Berkes, István
  • Hörmann, Siegfried
  • Schauer, Johannes

Abstract

We prove a strong invariance principle for the two-parameter empirical process of stationary sequences under a new weak dependence assumption. We give several applications of our results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:4:p:1298-1324
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    Cited by:

    1. Buchsteiner, Jannis, 2015. "Weak convergence of the weighted sequential empirical process of some long-range dependent data," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 170-179.
    2. Dominicy, Yves & Hörmann, Siegfried & Ogata, Hiroaki & Veredas, David, 2013. "On sample marginal quantiles for stationary processes," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 28-36.
    3. Jirak, Moritz, 2013. "A Darling–Erdös type result for stationary ellipsoids," Stochastic Processes and their Applications, Elsevier, vol. 123(6), pages 1922-1946.
    4. Guodong Pang & Ward Whitt, 2012. "The Impact of Dependent Service Times on Large-Scale Service Systems," Manufacturing & Service Operations Management, INFORMS, vol. 14(2), pages 262-278, April.
    5. Guodong Pang & Yuhang Zhou, 2018. "Two-parameter process limits for infinite-server queues with dependent service times via chaining bounds," Queueing Systems: Theory and Applications, Springer, vol. 88(1), pages 1-25, February.
    6. Phillips, Peter C.B. & Wang, Ying, 2022. "Functional coefficient panel modeling with communal smoothing covariates," Journal of Econometrics, Elsevier, vol. 227(2), pages 371-407.
    7. Wendler, Martin, 2016. "The sequential empirical process of a random walk in random scenery," Stochastic Processes and their Applications, Elsevier, vol. 126(9), pages 2787-2799.
    8. Moritz Jirak, 2016. "Optimal Rate of Convergence for Empirical Quantiles and Distribution Functions for Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(6), pages 825-836, November.
    9. Jirak, Moritz, 2012. "Change-point analysis in increasing dimension," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 136-159.
    10. Rademacher, Daniel & Kreiß, Jens-Peter & Paparoditis, Efstathios, 2024. "Asymptotic normality of spectral means of Hilbert space valued random processes," Stochastic Processes and their Applications, Elsevier, vol. 173(C).
    11. Lorenzo Ricci & David Veredas, 2012. "TailCoR," Working Papers 1227, Banco de España.
      • Sla{dj}ana Babi'c & Christophe Ley & Lorenzo Ricci & David Veredas, 2020. "TailCoR," Papers 2011.14817, arXiv.org.
    12. Ansgar Steland, 2016. "Asymptotics for random functions moderated by dependent noise," Statistical Inference for Stochastic Processes, Springer, vol. 19(3), pages 363-387, October.

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