Asymptotic normality of the ET method for extreme quantile estimation. Application to the ET test
Résumé
We investigate the asymptotic distribution of the Exponential Tail (ET) estimator of extreme quantiles. We give sufficient conditions for the asymptotic normality and provide some illustrating examples. Then, on the basis of this result, we propose a goodness-of-fit test for the tail of a usual distribution. The asymptotic power and level of the test are established.