Estimation of a scale second-order parameter related to the PORT methodology

Abstract

For heavy right tails and under a semiparametric framework, we introduce a class of location-invariant estimators of a scale second-order parameter and study its asymptotic nondegenerate behavior. This class is based on the PORT methodology, with PORT standing for peaks over random thresholds. The consistency and asymptotic normality of the new class of estimators is achieved under a third-order condition on the right tail of the underlying model F for intermediate and large ranks, respectively. An illustration of the finite sample behavior of the estimators is provided through a Monte Carlo simulation study.