Estimation of the conditional tail moment for Weibull-type distributions
Résumé
We consider the estimation of the conditional tail moment, defined for a positive random variable X as E[X^β |X > Q(1-p)], where Q denotes the quantile function of X, β > 0 and p \in (0, 1), at extreme levels for the class of Weibull-type distributions. A two-step procedure is introduced where in the first stage one estimates the conditional tail moment at an intermediate level, followed by an extrapolation in the second stage. The asymptotic properties of the estimators introduced in the two stages are derived under suitable assumptions.
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