Tail Index Estimation with Random Block Maxima

Details Tail Index Estimation with Random Block Maxima Tail Index Estimation with Random Block Maxima

2012-04-02

arxiv.org/abs/1204.0316v1

Statistics

Methodology

Scientific paper

Using a backtesting framework, we develop a new estimator for the tail index of a distribution in the Fr\'echet domain of attraction. This estimator is equivalent to taking a U-statistic over a Hill estimator with two order statistics. Our estimator presents multiple advantages over the Hill estimator. In particular, it has asymptotically C-infinity sample paths as a function of the threshold k, making it considerably more stable than the Hill estimator. Our estimator also admits a simple and intuitive threshold selection heuristic that requires neither fitting a second-order model nor choosing tuning parameters.

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