Kernel-type estimators for the extreme value index

• 成果类型: Article
• 署名作者: Groeneboom, P; Lopuhaä, HP; De Wolf, PP
• 署名单位: Delft University of Technology
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 2003
• 页码: 1956-1995
• 关键词: sample fraction; Tail Index; distributions; inference; bootstrap

摘要

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 quasi-maximum likelihood estimator. It has been generalized to a kernel-type estimator, but this kernel-type estimator can, similarly to the Hill estimator, only be used for the estimation of positive extreme value indices. In the present paper, we introduce kernel-type estimators which can be used for estimating the extreme value index over the whole (positive and negative) range. We present a number of results on their distributional behavior and compare their performance with the performance of other estimators, such as moment-type estimators for the whole range and the quasi-maximum likelihood estimator, based on the generalized Pareto distribution. We also discuss an automatic bandwidth selection method and introduce a kernel estimator for a second-order parameter, controlling the speed of convergence.