On Extreme Value Index Estimation under Random Censoring
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Extreme value analysis in the presence of censoring is receiving much attention as it has applications in many disciplines, including survival and reliability studies. Estimation of extreme value index (EVI) is of primary importance as it is a critical parameter needed in estimating extreme events such as quantiles and exceedance probabilities. In this paper, we review several estimators of the extreme value index when data is subject to random censoring. In addition, four estimators are proposed, one based on the exponential regression approximation of log spacings, one based on a Zipf estimator and two based on variants of the moment estimator. The proposed estimators and the existing ones are compared under the same simulation conditions. The performance measures for the estimators include confidence interval length and coverage probability. The simulation results show that no estimator is universally the best as the estimators depend on the size of the EVI parameter, percentage of censoring in the right tail and the underlying distribution. However, certain estimators such as the proposed reduced-bias estimator and the adapted moment estimator are found to perform well across most scenarios. Moreover, we present a bootstrap algorithm for obtaining samples for extreme value analysis in the context of censoring. Some of the estimators that performed well in the simulation study are illustrated using a practical dataset from medical research
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