Efficient estimators and LAN in canonical bivariate POT models |
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Authors: | Michael Falk Rolf-Dieter Reiss |
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Institution: | a Institut fuer Angewandte Mathematik und Statistik, Universitaet Wuerzburg, Am Hubland, Wuerzburg D-97074, Germany b Universitaet GH Siegen, Germany |
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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 ?∈0,1] of the GPs is provided by their canonical parameterization. We derive efficient estimators of ? and of the dependence function of the GP in various models and establish local asymptotic normality (LAN) of the loglikelihood function of a 2×2 table sorting of the observations. From this result we can deduce that the estimator of ? suggested by Falk and Reiss (2001, Statist. Probab. Lett. 52, 233-242) is not efficient, whereas a modification actually is. |
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Keywords: | 62H12 62H05 62G32 |
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