A Lynden-Bell integral estimator for extremes of randomly truncated data

This work deals with the estimation of the extreme value index and extreme quantiles for heavy tailed data, randomly right truncated by another heavy tailed variable. Under mild assumptions and the condition that the truncated variable is less heavy-tailed than the truncating variable, asymptotic normality is proved for both estimators. The proposed estimator of the extreme value index is an adaptation of the Hill estimator, in the natural form of a Lynden-Bell integral. Simulations illustrate the quality of the estimators under a variety of situations.