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 UU-statistic over a Hill estimator with two order statistics. The estimator presents multiple advantages over the Hill estimator. In particular, it has asymptotically C∞C∞ sample paths as a function of the threshold kk, 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.