Detecting influential data points for the Hill estimator in Pareto-type distributions

Authors:
Mia Hubert;Goedele Dierckx;Dina Vanpaemel
Affiliations:
KU Leuven, Department of Mathematics and Leuven Statistics Research Center (LStat), Celestijnenlaan 200B, BE-3001 Heverlee, Belgium;KU Leuven, Department of Mathematics and Leuven Statistics Research Center (LStat), Celestijnenlaan 200B, BE-3001 Heverlee, Belgium and Hogeschool-Universiteit Brussel, Stormstraat 2, BE-1000 Brus ...;KU Leuven, Department of Mathematics and Leuven Statistics Research Center (LStat), Celestijnenlaan 200B, BE-3001 Heverlee, Belgium
Venue:
Computational Statistics & Data Analysis
Year:
2013

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Abstract

Pareto-type distributions are extreme value distributions for which the extreme value index @c0. Classical estimators for @c0, like the Hill estimator, tend to overestimate this parameter in the presence of outliers. The empirical influence function plot, which displays the influence that each data point has on the Hill estimator, is introduced. To avoid a masking effect, the empirical influence function is based on a new robust GLM estimator for @c. This robust GLM estimator is used to determine high quantiles of the data generating distribution, allowing to flag data points as unusually large if they exceed this high quantile.