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Efficient estimators and LAN in canonical bivariate POT models

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  • Falk, Michael
  • Reiss, Rolf-Dieter
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    Abstract

    Bivariate generalized Pareto distributions (GPs) with uniform margins are introduced and elementary properties such as peaks-over-threshold (POT) stability are discussed. A unified parameterization with parameter [theta][set membership, variant][0,1] of the GPs is provided by their canonical parameterization. We derive efficient estimators of [theta] and of the dependence function of the GP in various models and establish local asymptotic normality (LAN) of the loglikelihood function of a 2x2 table sorting of the observations. From this result we can deduce that the estimator of [theta] suggested by Falk and Reiss (2001, Statist. Probab. Lett. 52, 233-242) is not efficient, whereas a modification actually is.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 84 (2003)
    Issue (Month): 1 (January)
    Pages: 190-207

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    Handle: RePEc:eee:jmvana:v:84:y:2003:i:1:p:190-207

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    Related research

    Keywords: Bivariate max-stable distribution Bivariate generalized Pareto distribution Dependence function Canonical parameterization Peaks-over-threshold stability BLUE LAN Hajek-LeCam convolution theorem Regular estimators;

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    Cited by:
    1. Falk, Michael & Reiss, Rolf-Dieter, 2005. "On the distribution of Pickands coordinates in bivariate EV and GP models," Journal of Multivariate Analysis, Elsevier, vol. 93(2), pages 267-295, April.
    2. Falk, Michael & Reiss, Rolf-Dieter, 2005. "On Pickands coordinates in arbitrary dimensions," Journal of Multivariate Analysis, Elsevier, vol. 92(2), pages 426-453, February.

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