Robustness properties of estimators in generalized Pareto Models

  • We study global and local robustness properties of several estimators for shape and scale in a generalized Pareto model. The estimators considered in this paper cover maximum likelihood estimators, skipped maximum likelihood estimators, moment-based estimators, Cramér-von-Mises Minimum Distance estimators, and, as a special case of quantile-based estimators, Pickands Estimator as well as variants of the latter tuned for higher finite sample breakdown point (FSBP), and lower variance. We further consider an estimator matching population median and median of absolute deviations to the empirical ones (MedMad); again, in order to improve its FSBP, we propose a variant using a suitable asymmetric Mad as constituent, and which may be tuned to achieve an expected FSBP of 34%. These estimators are compared to one-step estimators distinguished as optimal in the shrinking neighborhood setting, i.e., the most bias-robust estimator minimizing the maximal (asymptotic) bias and the estimator minimizing the maximal (asymptotic) MSE. For each of these estimators, we determine the FSBP, the influence function, as well as statistical accuracy measured by asymptotic bias, variance, and mean squared error—all evaluated uniformly on shrinking convex contamination neighborhoods. Finally, we check these asymptotic theoretical findings against finite sample behavior by an extensive simulation study.

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Metadaten
Verfasserangaben:P. Ruckdeschel, N. Horbenko
URN (Permalink):urn:nbn:de:hbz:386-kluedo-16473
Schriftenreihe (Bandnummer):Berichte des Fraunhofer-Instituts für Techno- und Wirtschaftsmathematik (ITWM Report) (182)
Dokumentart:Bericht
Sprache der Veröffentlichung:Englisch
Jahr der Fertigstellung:2010
Jahr der Veröffentlichung:2010
Veröffentlichende Institution:Fraunhofer-Institut für Techno- und Wirtschaftsmathematik
Datum der Publikation (Server):21.07.2010
Freies Schlagwort / Tag:finite sample breakdown point ; generalized Pareto distribution; global robustness ; local robustness
Fachbereiche / Organisatorische Einheiten:Fraunhofer (ITWM)
DDC-Sachgruppen:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Lizenz (Deutsch):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011

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