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Efficient estimators and LAN in canonical bivariate POT models

Listed author(s):
  • Falk, Michael
  • Reiss, Rolf-Dieter
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    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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    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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    1. Drees, Holger & Huang, Xin, 1998. "Best Attainable Rates of Convergence for Estimators of the Stable Tail Dependence Function," Journal of Multivariate Analysis, Elsevier, vol. 64(1), pages 25-47, January.
    2. Falk, Michael & Reiss, Rolf-Dieter, 2001. "Estimation of canonical dependence parameters in a class of bivariate peaks-over-threshold models," Statistics & Probability Letters, Elsevier, vol. 52(3), pages 233-242, April.
    3. Lu, Jye-Chyi & Bhattacharyya, Gouri K., 1991. "Inference procedures for bivariate exponential model of Gumbel," Statistics & Probability Letters, Elsevier, vol. 12(1), pages 37-50, July.
    4. E. Kaufmann & R. Reiss, 1993. "Strong convergence of multivariate point processes of exceedances," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 45(3), pages 433-444, September.
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