A Robust Estimator of the Tail Index Based on an Exponential Regression Model

Abstract

The objectives of a robust statistical analysis and of all extreme value analysis apparently are contradictory. Where the extreme data are downweighted in robust statistics, these observations receive most attention in an extreme value approach. The most prominent extreme value methods however are constructed on maximum likelihood estimates based on specific parametric models which are fitted to exceedances over large thresholds. So within an extreme value framework some robust algorithms replacing the maximum likelihood part of this methodology can be of use leading to estimates which are less sensitive to few particular observations. This study is motivated by a soil database quality management project, where in the background of Pareto-type tails, automatic identification of suspicious data is needed.