Statistical analysis of extreme values
Statistical analysis of extreme values
Best attainable rates of convergence for estimators of the stable tail dependence function
Journal of Multivariate Analysis
On the distribution of Pickands coordinates in bivariate EV and GP models
Journal of Multivariate Analysis
On Pickands coordinates in arbitrary dimensions
Journal of Multivariate Analysis
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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 θ ∈ [0, 1] of the GPs is provided by their canonical parameterization. We derive efficient estimators of θ 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 θ suggested by Falk and Reiss (2001, Statist. Probab. Lett. 52, 233-242) is not efficient, whereas a modification actually is.