Efficient estimators and LAN in canonical bivariate POT models

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.