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Asymptotic expansions for the location invariant moment-type estimator

Author

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  • Zuoxiang, Peng
  • Miaomiao, Liu
  • Nadarajah, Saralees

Abstract

In this paper, based on moment-type and location invariant Hill estimators, a new kind of location invariant moment-type extreme value index estimator is proposed. The weak and strong consistency of the estimator are discussed. The asymptotic expansion of the estimator and its distribution are also considered under second order regularly varying conditions. The asymptotic normality is employed to construct the confidence interval. Monte Carlo simulations are performed to compare the Hill estimator and the moment estimator in terms of mean squared error.

Suggested Citation

  • Zuoxiang, Peng & Miaomiao, Liu & Nadarajah, Saralees, 2010. "Asymptotic expansions for the location invariant moment-type estimator," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(5), pages 982-998.
    • Handle: RePEc:eee:matcom:v:80:y:2010:i:5:p:982-998
    DOI: 10.1016/j.matcom.2009.12.002
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    References listed on IDEAS

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    3. 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.
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    5. McNeil, Alexander J., 1997. "Estimating the Tails of Loss Severity Distributions Using Extreme Value Theory," ASTIN Bulletin, Cambridge University Press, vol. 27(1), pages 117-137, May.
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