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We revisit the estimation of the extreme value index for randomly censoreddata from a heavy tailed distribution. We introduce a new class of estimatorswhich encompasses earlier proposals given in Worms and Worms (2014) andBeirlant et al. (2018), which were shown to have good bias properties comparedwith the pseudo maximum likelihood estimator proposed in Beirlant et al. (2007)and Einmahl et al. (2008). However the asymptotic normality of the type ofestimators first proposed in Worms and Worms (2014) was still lacking, in therandom threshold case. We derive an asymptotic representation and theasymptotic normality of the larger class of estimators and consider theirfinite sample behaviour. Special attention is paid to the case of heavycensoring, i.e. where the amount of censoring in the tail is at least 50\%. Weobtain the asymptotic normality with a classical $\sqrt{k}$ rate where $k$denotes the number of top data used in the estimation, depending on the degreeof censoring.

Estimation of the extreme value index in a censorship framework: asymptotic and finite sample behaviour