Purpose: To propose methods for the detection of highly influential data points for the Hill estimator in Pareto-type distributions. Summary: It is discussed about the Pareto-type distributions (or heavy tailed distributions) that are extreme value distributions for which the extreme value index is the lone parameter. It is argued that the classical estimators like the Hill estimator tend to overestimate this parameter in the presence of outliers. In this regard, the empirical influence function plot, which displays the influence that each data point has on the Hill estimator, is introduced. In fact, the empirical influence function is based on a new robust CLM estimator of the parameter of interest. In this regard, the Hill estimator is reviewed and its influence function and empirical influence function are derived. The robust GLM estimator and other aspects for parameter are studied in detail. Using the robust CLM estimator the high quantiles for the data generating distribution in a robust way are derived and are combined with the empirical influence function on a diagnostic plot to visualize which data points are unusually large and are highly influential for the Hill estimator. The performance of the robust GLM estimator is illustrated using a simulation study. In order to illustrate the proposed method a real data set is used. (37 refs.)
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