Efficient estimators and LAN in canonical bivariate POT models

Michael Falk and Rolf-Dieter Reiss

Journal of Multivariate Analysis, 2003, vol. 84, issue 1, 190-207

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 [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.

Keywords: Bivariate; max-stable; distribution; Bivariate; generalized; Pareto; distribution; Dependence; function; Canonical; parameterization; Peaks-over-threshold; stability; BLUE; LAN; Hajek-LeCam; convolution; theorem; Regular; estimators (search for similar items in EconPapers)
Date: 2003
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Citations: View citations in EconPapers (2)

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