Tail Index Estimation with Random Block Maxima

Using a backtesting framework, we develop a new estimator for the tail index of a distribution in the Frechet domain of attraction. 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 smooth 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 heuristic that does not require fitting a second-order model.