Generalized Kernel Estimators for the Weibull-Tail Coefficient |
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| Authors: | Yuri Goegebeur Jan Beirlant Tertius De Wet |
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| Affiliation: | 1. Department of Mathematics and Computer Science , University of Southern Denmark , Odense M, Denmark yuri.goegebeur@stat.sdu.dk;3. Department of Mathematics and Leuven Statistics Research Centre , K.U. Leuven, Heverlee, Belgium;4. Department of Statistics and Actuarial Science , University of Stellenbosch , Stellenbosch, South Africa |
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| Abstract: | We introduce new families of estimators for the Weibull-tail coefficient, obtained from a weighted sum of a power transformation of excesses over a high random threshold. Asymptotic normality of the estimators is proven for an intermediate sequence of upper order statistics, and under classical regularity conditions for L-statistics and a second-order condition on the tail behavior of the underlying distribution. The small sample performance of two specific examples of kernel functions is evaluated in a simulation study. |
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| Keywords: | Kernel statistics Weibull-type distribution Weibull-tail coefficient |
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