A Sliding Blocks Estimator for the Extremal Index

TL;DR

This paper compares disjoint and sliding blocks estimators for the extremal index in extreme value statistics, demonstrating the superior efficiency and lower bias of the sliding blocks approach, along with a bias reduction method.

Contribution

It introduces a bias reduction technique for the sliding blocks estimator and compares its asymptotic properties to the disjoint blocks estimator.

Findings

Sliding blocks estimator is more efficient than disjoint blocks.

Sliding blocks estimator has smaller asymptotic bias.

Proposed bias reduction method improves estimation accuracy.

Abstract

In extreme value statistics for stationary sequences, blocks estimators are usually constructed by using disjoint blocks because exceedances over high thresholds of different blocks can be assumed asymptotically independent. In this paper we focus on the estimation of the extremal index which measures the degree of clustering of extremes. We consider disjoint and sliding blocks estimators and compare their asymptotic properties. In particular we show that the sliding blocks estimator is more efficient than the disjoint version and has a smaller asymptotic bias. Moreover we propose a method to reduce its bias when considering sufficiently large block sizes.