Weak properties and robustness of t-Hill estimators

Abstract : We describe a novel method of heavy tails estimation based on transformed score (t-score). Based on a new score moment method we derive the t-Hill estimator, which estimates the extreme value index of a distribution function with regularly varying tail. t-Hill estimator is distribution sensitive, thus it differs in e.g. Pareto and log-gamma case. Here, we study both forms of the estimator, i.e. t-Hill and t-lgHill. For both estimators we prove weak consistency in moving average settings as well as the asymptotic normality of t-lgHill estimator in iid setting. In cases of contamination with heavier tails than the tail of original sample, t-Hill outperforms several robust 2 P. Jordanova et al. tail estimators, especially in small samples. A simulation study emphasizes the fact that the level of contamination is playing a crucial role. The larger the contamination, the better are the t-score moment estimates. The reason for this is the bounded t-score of heavy-tailed distributions (and, consequently, bounded influence functions of the estimators). We illustrate the developed methodology on a small sample data set of stake measurements from Guanaco glacier in Chile.
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Extremes, Springer Verlag (Germany), 2016, 19 (4), pp.591--626. 〈10.1007/s10687-016-0256-2〉
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Pavlina Jordanova, Zdeněk Fabián, Philipp Hermann, Lubos Strelec, Andrés Rivera, et al.. Weak properties and robustness of t-Hill estimators. Extremes, Springer Verlag (Germany), 2016, 19 (4), pp.591--626. 〈10.1007/s10687-016-0256-2〉. 〈hal-01327002〉

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