Weak Properties and Robustness of t-Hill Estimators

0460584 - ÚI 2017 RIV US eng J - Journal Article
Jordanova, P. - Fabián, Zdeněk - Hermann, P. - Střelec, L. - Rivera, A. - Girard, S. - Torres, S. - Stehlík, M.
Weak Properties and Robustness of t-Hill Estimators.
Extremes. Roč. 19, č. 4 (2016), s. 591-626. ISSN 1386-1999. E-ISSN 1572-915X
Institutional support: RVO:67985807
Keywords : asymptotic properties of estimators * point estimation * t-Hill estimator * t-lgHill estimator
Subject RIV: BB - Applied Statistics, Operational Research
Impact factor: 1.679, year: 2016

e 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.
Permanent Link: http://hdl.handle.net/11104/0260616