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Asymptotic Normality of Extreme Value Estimators on C[0,1]

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  • Einmahl, J.H.J.

    (Tilburg University, Center For Economic Research)

  • Lin, T.

Abstract

Consider n i.i.d. random elements on C[0; 1].We show that under an appropriate strengthening of the domain of attraction condition natural estimators of the extreme-value index, which is now a continuous function, and the normalizing functions have a Gaussian process as limiting distribution.A key tool is the weak convergence of a weighted tail empirical process, which makes it possible to obtain the results uniformly on [0; 1].Detailed examples are also presented.
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Suggested Citation

  • Einmahl, J.H.J. & Lin, T., 2003. "Asymptotic Normality of Extreme Value Estimators on C[0,1]," Discussion Paper 2003-132, Tilburg University, Center for Economic Research.
    • Handle: RePEc:tiu:tiucen:9565e7d8-72fd-4de8-8643-b18367b70d68
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    References listed on IDEAS

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    1. Einmahl, J. H.J. & Dekkers, A. L.M. & de Haan, L., 1989. "A moment estimator for the index of an extreme-value distribution," Other publications TiSEM 81970cb3-5b7a-4cad-9bf6-2, Tilburg University, School of Economics and Management.
    2. Holger Drees, 1998. "On Smooth Statistical Tail Functionals," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 25(1), pages 187-210, March.
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    Cited by:

    1. Robert, Christian Y., 2022. "Testing for changes in the tail behavior of Brown–Resnick Pareto processes," Stochastic Processes and their Applications, Elsevier, vol. 144(C), pages 312-368.
    2. de Valk, Cees, 2016. "A large deviations approach to the statistics of extreme events," Other publications TiSEM 117b3ba0-0e40-4277-b25e-d, Tilburg University, School of Economics and Management.
    3. Einmahl, John & Segers, Johan, 2020. "Empirical Tail Copulas for Functional Data," Other publications TiSEM edc722e6-cc70-4221-87a2-8, Tilburg University, School of Economics and Management.
    4. Einmahl, J.H.J. & Khmaladze, E.V., 2007. "Central Limit Theorems For Local Emprical Processes Near Boundaries of Sets," Other publications TiSEM c4c26f2d-99d3-473f-9900-e, Tilburg University, School of Economics and Management.

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