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This paper addresses the problem of estimating the extreme value index inpresence of random censoring for distributions in the Weibull domain ofattraction. The methodologies introduced in [Worms (2014)], in the heavy-tailedcase, are adapted here to the negative extreme value index framework, leadingto the definition of weighted versions of the popular moments of relativeexcesses with arbitrary exponent. This leads to the definition of two familiesof estimators (with an adaptation of the so called Moment estimator as aparticular case), for which the consistency is proved under a first ordercondition. Illustration of their performance, issued from an extensivesimulation study, are provided.

Moment estimators of the extreme value index for randomly censored data in the Weibull domain of attraction