Kernel-type estimators for the extreme value index. (English) Zbl 1047.62046

Groeneboom, P.; Lopuhaä, H. P.; de Wolf, P. P.

Ann. Stat. 31, No. 6, 1956-1995 (2003).

The paper deals with the estimation of the shape parameter \(\gamma\) of the generalized extreme value distribution. The parameter \(\gamma\) is known also as the extreme value index or the tail index. The authors propose kernel-type estimators which can be used for estimating the extreme value index over the whole (positive and negative) range. A number of results on consistency and asymptotic normality of the estimators are presented. The obtained kernel-type estimators are compared with other known estimators. The automatic choice of the bandwidth is also discussed.

Reviewer: Wiesław Dziubdziela (Kielce)

MSC:

62G32	Statistics of extreme values; tail inference
62G20	Asymptotic properties of nonparametric inference
62G05	Nonparametric estimation

Keywords:

extreme value index; adaptive estimation; second order parameter estimation

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