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Bias Correction for the Maximum Likelihood Estimator of the Extreme Value Index
Dr Xuan Leng
Department of Statistics and Applied Probability, NUS
Friday 21 September 2018, 04:30pm - 05:30pm
S16-06-118, Seminar Room

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.