Multiple thresholds in extremal parameter estimation

Selecting the number of upper order statistics to use in extremal inference or selecting the threshold above which we perform the extremal inference is a common step in applications of extreme value theory. Not only is the selection itself difficult, but the large part of the sample below the threshold may potentially carry useful information. We propose an approach that takes an extremal parameter estimator and modifies it to allow for using multiple thresholds instead of a single one. We apply this approach to the problem of estimating the extremal index and demonstrate its power both on simulated and real data.