Consistency of the ET method and smooth
نویسنده
چکیده
We deene the kth order estimate of an extreme quantile q n , n < 1=n, and study its consistency as n ! 0 and n ! 1 for classes of distributions in the maximum domain of attraction of Gumbel. We show that the consistency of the kth order estimate imposes conditions on n in most cases, but does not depend on its order k. As a particular case, we obtain that, when the ET estimate (which is also the rst-order estimate) is consistent, then the quantile q n can also be consistently estimated by the maximal observation. When an esti-mator is consistent, we give the rate of convergence to zero of the relative approximation error.
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