Subsampling extremes: From block maxima to smooth tail estimation

We study a new estimator for the tail index of a distribution in the Fréchet domain of attraction that arises naturally by computing subsample maxima. This estimator is equivalent to taking a U -statistic over a Hill estimator with two order statistics. The estimator presents multiple advantages over the Hill estimator. In particular, it has asymptotically C ∞ sample paths as a function of the threshold k , making it considerably more stable than the Hill estimator. The estimator also admits a simple and intuitive threshold selection rule that does not require fitting a second-order model.