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Title: Asymptotic distributions of linear and non linear combinations of extreme order statistics
Keywords: Asymptotic normality
sums of extreme values
extreme order statistics
extreme squared deviation
quantile process
tails distributions
Issue Date: 29-Dec-2013
Abstract: The limit distributions of linear and non-linear combinations of the kn = o(n) order statistics of i.i.d. random variables whose maximum belongs to the domain of attraction of the Gumbel law are obtained. Our results may be applied in actuarial studies, estimation of scale-location parameters, estimation of squared deviation in tail of a distribution, robustness theory and detection of the outliers in statistical data. It is also closely related to the moment estimator of Dekkers-Einmahl-de Hann (1989) for the index of an extreme distribution. This study completes that of Necir (1990, 1991a, 1991b, 2000a, 2000b).
Appears in Collections:CS N 03

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