Estimation of the third-order parameter in extreme value statistics
We introduce a class of estimators for the third-order parameter in extreme value statistics when the distribution function underlying the data is heavy tailed. For appropriately chosen intermediate sequences of upper order statistics, consistency is established under the third-order tail condition and asymptotic normality under the fourth-order tail condition. Simulation experiments illustrate the finite sample behavior of some selected estimators. © 2011 Sociedad de Estadística e Investigación Operativa.