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Weak properties and robustness of t-Hill estimators
AuthorJordanova, Pavlina ; Fabián, Zdeněk ; Hermann, Philipp ; Střelec, Luboš ; Rivera, Andrés ; Girard, Stéphane ; Torres, Sebastián ; Stehlík, Milan
Published in
Extremes, 2016, Vol. 19, Issue 4, page 591-626
PublishedSpringer, 2016
Document typeJournal Article
Keywords (EN)Point estimation / Asymptotic properties of estimators / t-Hill estimator / t-lgHill estimator
URNurn:nbn:at:at-ubl:3-1397 Persistent Identifier (URN)
 The work is publicly available
Weak properties and robustness of t-Hill estimators [2 mb]
Abstract (English)

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 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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