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Asymptotics for statistical functionals of long-memory sequences

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  • Beutner, Eric
  • Wu, Wei Biao
  • Zähle, Henryk

Abstract

We present two general results that can be used to obtain asymptotic properties for statistical functionals based on linear long-memory sequences. As examples for the first one we consider L- and V-statistics, in particular tail-dependent L-statistics as well as V-statistics with unbounded kernels. As an example for the second result we consider degenerate V-statistics. To prove these results we also establish a weak convergence result for empirical processes of linear long-memory sequences, which improves earlier ones.

Suggested Citation

  • Beutner, Eric & Wu, Wei Biao & Zähle, Henryk, 2012. "Asymptotics for statistical functionals of long-memory sequences," Stochastic Processes and their Applications, Elsevier, vol. 122(3), pages 910-929.
    • Handle: RePEc:eee:spapps:v:122:y:2012:i:3:p:910-929
    DOI: 10.1016/j.spa.2011.10.006
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    4. Beutner, Eric & Zähle, Henryk, 2010. "A modified functional delta method and its application to the estimation of risk functionals," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2452-2463, November.
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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. Krätschmer Volker & Schied Alexander & Zähle Henryk, 2015. "Quasi-Hadamard differentiability of general risk functionals and its application," Statistics & Risk Modeling, De Gruyter, vol. 32(1), pages 25-47, April.
    3. Henryk Zähle, 2014. "Qualitative robustness of von Mises statistics based on strongly mixing data," Statistical Papers, Springer, vol. 55(1), pages 157-167, February.
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    6. Volker Kratschmer & Alexander Schied & Henryk Zahle, 2014. "Quasi-Hadamard differentiability of general risk functionals and its application," Papers 1401.3167, arXiv.org, revised Feb 2015.

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