A Sliding Blocks Estimator for the Extremal Index

Details A Sliding Blocks Estimator for the Extremal Index A Sliding Blocks Estimator for the Extremal Index

2008-12-22

arxiv.org/abs/0812.4233v1

Mathematics

Statistics Theory

Submitted to the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics

Scientific paper

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.

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