A Hill Type Estimator of the Weibull Tail-Coefficient

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Conditional extremes from heavy-tailed distributions: an application to the estimation of extreme rainfall return levels (2010, unknown): “Moreover, under (B), it is well-known that k 1/2 t ((mt/kt)Vkt,mt − 1) d → N (0, 1), (see for instance (Girard 2004)) and thus ζ1,n = OP(∆tk −1/2 t ) + OP(ωn(m −(1+δ) t )).”
Bias-reduced estimators of the Weibull tail-coefficient (2008, unknown): “In Girard (2004), the asymptotic normality of θ n is established under suitable assumptions. e This assumption can be expressed in terms of the slowly varying function ` as follows: To prove such a result, a second-order condition is required in order to specify the bias-term.”
Weibull tail-distributions revisited: a new look at some tail estimators (2011, background): “More specifically, most recent estimators are based on the log-spacings between the kn upper order statistics [7, 11, 22, 23, 25, 26, 27].”