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Weak Properties and Robustness of t-Hill Estimators
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SYSNO ASEP 0460584 Druh ASEP J - Článek v odborném periodiku Zařazení RIV J - Článek v odborném periodiku Poddruh J Článek ve WOS Název Weak Properties and Robustness of t-Hill Estimators Tvůrce(i) Jordanova, P. (BG)
Fabián, Zdeněk (UIVT-O) SAI, RID
Hermann, P. (AT)
Střelec, L. (CZ)
Rivera, A. (CL)
Girard, S. (FR)
Torres, S. (FR)
Stehlík, M. (AT)Zdroj.dok. Extremes. - : Springer - ISSN 1386-1999
Roč. 19, č. 4 (2016), s. 591-626Poč.str. 36 s. Jazyk dok. eng - angličtina Země vyd. US - Spojené státy americké Klíč. slova asymptotic properties of estimators ; point estimation ; t-Hill estimator ; t-lgHill estimator Vědní obor RIV BB - Aplikovaná statistika, operační výzkum Institucionální podpora UIVT-O - RVO:67985807 UT WOS 000386530500002 EID SCOPUS 84976293899 DOI 10.1007/s10687-016-0256-2 Anotace 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. Pracoviště Ústav informatiky Kontakt Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Rok sběru 2017
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