Robust estimations for the tail index of Weibull-type distribution
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Based on suitable left-truncated and censored transformation of the underlying risks, two classes of M-estimations of Weibull tail coefficient are proposed. These estimations are highly flexible and less sensitive to extreme contaminations with two flexible thresholds bounding the psi-function. Asymptotic normality with √(n)-rate of convergence is obtained at the cost of bounded asymptotic bias. The choice of flexible threshold is discussed with the asymptotic relative efficiency and influence function taken into considerations. A small scale of simulations show the robustness and stability of these estimations even for small samples.
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