Adaptive PORT-MVRB Estimation of the Extreme Value Index

Abstract

In this chapter, we consider an application to environmental data of a bootstrap algorithm for the adaptive estimation of the extreme value index (EVI), the primary parameter in Statistics of Extremes. The EVI estimation is performed through the recent Peaks Over Random Threshold Minimum-Variance Reduced-Bias (PORT-MVRB) estimators, which apart from scale invariant, like the classical ones, are also location invariant. These estimators depend not only on an integer tuning parameter k, the number of top order statistics involved in the estimation, but also on an extra control real parameter q, 0 ≤ q < 1, which makes them highly flexible.