Academic

A key step in extreme value statistics is to accurately estimate the extreme value index, which characterizes the shape of the tail region of a distribution function. However, the generally used maximum likelihood estimator (MLE) suffers from an asymptotic bias. This paper conducts bias correction for the MLE. The bias corrected estimator allows for using more high order statistics, which results in a lower asymptotic variance compared to the MLE. Particularly, it is more flexible in choosing the number of high order statistics for finite sample application. Extensive simulations conform the advantages and we apply our estimator to test whether human life span is unlimited.