B1710
Title: Statistical inference for the local dependence condition in extreme value estimation
Authors: Jan Holesovsky - Brno University of Technology (Czech Republic) [presenting]
Michal Fusek - Brno University of Technology (Czech Republic)
Abstract: From the theory, it follows that the local dependence in a stationary series causes clustering of extreme values. Hence, the inference for extremes typically requires proper identification of clusters of high threshold exceedances. This involves a suitable estimator of the extremal index which is the primary measure of the local dependence. Most estimators of the extremal index are derived under further restrictions on the dependence structure of the clusters. Such restriction represents the $D^{(k)}(u_n)$ condition that controls the tendency of the process to obtain a threshold non-exceedance within a cluster. Namely, the $D^{(2)}(u_n)$ condition is often assumed. However, an extremal index estimator based on a particular condition is inappropriate for other processes, leading to possibly high bias if the condition is not satisfied. Some recent estimators (e.g. the $K$-gap or the truncated estimators) suppose the case of a general $k$. The properties and the suitability are managed by the selection of auxiliary parameters. At the time, there is no suitable methodology available to assess the order $k$ of the local dependence condition. Some suggestions based on graphical diagnostics were made earlier, but these are often rather subjective. In this contribution, a novel approach is presented for the assessment of the proper condition $D^{(k)}(u_n)$, and hence the selection of auxiliary parameters, via the censored and the truncated estimators of the extremal index.
