PORT-ESTIMATION OF A SHAPE SECOND-ORDER PARAMETER

• In this paper we study, under a semi-parametric framework and for heavy right tails, a class of location invariant estimators of a shape second-order parameter, ruling the rate of convergence of the normalised sequence of maximum values to a non-degenerate limit. This class is based on the PORT methodology, with PORT standing for peaks over random thresholds. Asymptotic normality of such estimators is achieved under a third-order condition on the right-tail of the underlying model F and for suitable large intermediate ranks. An illustration of the finite sample behaviour of the estimators is provided through a small-scale Monte-Carlo simulation study. Key-Words: • asymptotic properties; location/scale invariant estimation; Monte-Carlo simulation; PORT methodology; sample of excesses; semi-parametric estimation; shape secondorder parameters; statistics of extremes; third-order framework. AMS Subject Classification: • 62G32, 62E20; 65C05. 300 L. Henriques-Rodrigues, M.I. Gomes, M.I. Fraga Alves and C. Neves PORT-Estimation of a Shape Second-Order Parameter 301

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