Refined Pickands estimators of the extreme value index
نویسندگان
چکیده
منابع مشابه
Generalized Pickands estimators for the extreme value index
The Pickands estimator for the extreme value index is generalized in a way that includes all of its previously known variants. A detailed study of the asymptotic behavior of the estimators in the family serves to determine its optimally performing members. These are given by simple, explicit formulas, have the same asymptotic variance as the maximum likelihood estimator in the generalized Paret...
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− One of the main goals of extreme value analysis is to estimate the probability of rare events given a sample from an unknown distribution. The upper tail behavior of this distribution is described by the extreme value index. We present a new estimator of the extreme value index adapted to any domain of attraction. Its construction is similar to the one of Pickands’ estimator. Its weak consist...
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This paper presents new approaches for the estimation of the extreme value index in the framework of randomly censored (from the right) samples, based on the ideas of Kaplan-Meier integration and the synthetic data approach of S.Leurgans (1987). These ideas are developed here in the heavy tail case and for the adaptation of the Hill estimator, for which the consistency is proved under first ord...
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The maximum likelihood method offers a standard way to estimate the three parameters of a generalized extreme value (GEV) distribution. Combined with the block maxima method, it is often used in practice to assess the extreme value index and normalization constants of a distribution satisfying a first order extreme value condition, assuming implicitely that the block maxima are exactly GEV dist...
متن کاملKernel-type Estimators for the Extreme Value Index by P. Groeneboom,
A large part of the theory of extreme value index estimation is developed for positive extreme value indices. The best-known estimator of a positive extreme value index is probably the Hill estimator. This estimator belongs to the category of moment estimators, but can also be interpreted as a quasimaximum likelihood estimator. It has been generalized to a kernel-type estimator, but this kernel...
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ژورنال
عنوان ژورنال: The Annals of Statistics
سال: 1995
ISSN: 0090-5364
DOI: 10.1214/aos/1034713647