Estimation of the Third Order Parameter in Extreme Value Statistics
Yuri Goegebeur1, Tertius de Wet2
1Department of Mathematics and Computer Science, University of Southern Denmark, Denmark; 2Department of Statistics and Actuarial Science, Stellenbosch University, South Africa

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. The third order parameter determines the rate of convergence in the second order framework, and the estimation of it is of practical relevance for (i) obtaining bias-reduced estimators for the second order parameter and (ii) the selection of the number of extreme values to be used in the estimation of the second order parameter. We show that for appropriately chosen intermediate sequences of upper order statistics, the estimators for the third order parameter are consistent under the third order tail condition, and asymptotically normal under the fourth order tail condition. Numerical and simulation experiments illustrate the asymptotic and finite sample behavior, respectively, of some selected estimators.

Keywords: Pareto-type distribution; third order parameter; fourth order tail condition

Biography: Yuri Goegebeur is appointed as associate professor at the Department of Mathematics and Computer Science of the University of Southern Denmark. He obtained his PhD in Science - Mathematics at the Catholic University of Leuven (Belgium). His research interests are in the area of extreme value statistics where he works on the estimation of first and higher order tail parameters.