In extreme value analysis, the extreme value index plays a vital role as itdetermines the tail heaviness of the underlying distribution and is the primaryparameter required for the estimation of other extreme events. In this paper,we review the estimation of the extreme value index when observations aresubject to right random censoring and the presence of covariate information. Inaddition, we propose some estimators of the extreme value index, including amaximum likelihood estimator from a perturbed Pareto distribution. The existingestimators and the proposed ones are compared through a simulation study underidentical conditions. The results show that the performance of the estimatorsdepend on the percentage of censoring, the underlying distribution, the size ofextreme value index and the number of top order statistics. Overall, we foundthe proposed estimator from the perturbed Pareto distribution to be robust tocensoring, size of the extreme value index and the number of top orderstatistics.
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