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Estimating the parameters of rare events

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  • Hsing, Tailen

Abstract

In this paper the estimation of certain parameters of the extreme order statistics of stationary observations is considered in a general framework. These parameters are resulted from dependence, and hence their inference is substantially different from similar considerations in the i.i.d. context. Variants of estimators that are functionals of the empirical 'cluster size' distribution are proposed, and such properties as consistency and asymptotic normality are studied. Special emphasis is given to estimating the extremal index.

Suggested Citation

  • Hsing, Tailen, 1991. "Estimating the parameters of rare events," Stochastic Processes and their Applications, Elsevier, vol. 37(1), pages 117-139, February.
  • Handle: RePEc:eee:spapps:v:37:y:1991:i:1:p:117-139
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    Cited by:

    1. Jose Olmo, 2015. "A New Family of Consistent and Asymptotically-Normal Estimators for the Extremal Index," Econometrics, MDPI, Open Access Journal, vol. 3(3), pages 1-21, August.
    2. Davis, Richard A. & Mikosch, Thomas & Zhao, Yuwei, 2013. "Measures of serial extremal dependence and their estimation," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2575-2602.
    3. Jondeau, Eric & Rockinger, Michael, 2003. "Testing for differences in the tails of stock-market returns," Journal of Empirical Finance, Elsevier, vol. 10(5), pages 559-581, December.
    4. Segers, J.J.J., 2003. "Approximate Distributions of Clusters of Extremes," Discussion Paper 2003-91, Tilburg University, Center for Economic Research.
    5. Segers, Johan, 2005. "Approximate distributions of clusters of extremes," Statistics & Probability Letters, Elsevier, vol. 74(4), pages 330-336, October.
    6. Bertrand B. Maillet & Jean-Philippe R. M�decin, 2010. "Extreme Volatilities, Financial Crises and L-moment Estimations of Tail-indexes," Working Papers 2010_10, Department of Economics, University of Venice "Ca' Foscari".
    7. Jalal, Amine & Rockinger, Michael, 2008. "Predicting tail-related risk measures: The consequences of using GARCH filters for non-GARCH data," Journal of Empirical Finance, Elsevier, vol. 15(5), pages 868-877, December.
    8. Olmo, J., 2006. "A new family of estimators for the extremal index," Working Papers 06/01, Department of Economics, City University London.

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