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

作者：Hubert Mia^*; Dierckx Goedele; Vanpaemel Dina

来源：Computational Statistics & Data Analysis, 2013, 65: 13-28.

DOI：10.1016/j.csda.2012.07.011

• Pareto-type distribution
• Extreme value index
• Tail index estimation
• Influential data points
• Robustness

Pareto-type distributions are extreme value distributions for which the extreme value index gamma > 0. Classical estimators for gamma > 0, 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 gamma. 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.

• 出版日期2013-9