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 thetais an element of[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 2 x 2 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. (C) 2003 Elsevier Science (USA). All rights reserved.