Asymptotic normality of extreme value estimators on C[0,1]

• 成果类型: Article
• 署名作者: Einmahl, John H. J.; Lin, Tao
• 署名单位: Tilburg University; Xiamen University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053605000000831
• 发表日期: 2006
• 页码: 469-492
• 关键词: index

摘要

Consider n i.i.d. random elements on C[0, 1]. We show that, under an appropriate strengthening of the domain of attraction condition, natural estimators of the extreme-value index, which is now a continuous function, and the normalizing functions have a Gaussian process as limiting distribution. A key tool is the weak convergence of a weighted tail empirical process, which makes it possible to obtain the results uniformly on [0, 1]. Detailed examples are also presented.