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Asymptotics for statistical functionals of long-memory sequences

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

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    Bibliographic Info

    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 122 (2012)
    Issue (Month): 3 ()
    Pages: 910-929

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    Handle: RePEc:eee:spapps:v:122:y:2012:i:3:p:910-929

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    Related research

    Keywords: Noncentral limit theorem; Linear long-memory sequence; Quasi-Hadamard differentiability; Modified Functional Delta Method; Weighted empirical process; L-statistic; U- and V-statistics; Degenerate V-statistic;

    References

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    1. 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.
    2. Chen, Xiaohong & Fan, Yanqin, 2006. "Estimation of copula-based semiparametric time series models," Journal of Econometrics, Elsevier, vol. 130(2), pages 307-335, February.
    3. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
    4. Lavancier, Frédéric & Philippe, Anne & Surgailis, Donatas, 2010. "A two-sample test for comparison of long memory parameters," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2118-2136, October.
    5. Wang, Shaun & Dhaene, Jan, 1998. "Comonotonicity, correlation order and premium principles," Insurance: Mathematics and Economics, Elsevier, vol. 22(3), pages 235-242, July.
    6. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
    7. Koul, Hira L. & Surgailis, Donatas, 2001. "Asymptotics of empirical processes of long memory moving averages with infinite variance," Stochastic Processes and their Applications, Elsevier, vol. 91(2), pages 309-336, February.
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    Cited by:
    1. Henryk Zähle, 2014. "Qualitative robustness of von Mises statistics based on strongly mixing data," Statistical Papers, Springer, vol. 55(1), pages 157-167, February.
    2. Volker Kr\"atschmer & Alexander Schied & Henryk Z\"ahle, 2014. "Quasi-Hadamard differentiability of general risk functionals and its application," Papers 1401.3167, arXiv.org.

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