Weighted approximations of tail processes for β-mixing random variables

• 成果类型: Article
• 署名作者: Drees, H
• 署名单位: Ruprecht Karls University Heidelberg
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• 发表日期: 2000
• 页码: 1274-1301
• 关键词: index estimation; dependent data; statistics; inference; SEQUENCES; models

摘要

While the extreme value statistics for i.i.d data is well developed, much less is known about the asymptotic behavior of statistical procedures in the presence of dependence. We establish convergence of the tail empirical processes to Gaussian limits for beta -mixing stationary time series. As a consequence, one obtains weighted approximations of the tail empirical quantile function that is based on a random sequence with marginal distribution belonging to the domain of attraction of an extreme value distribution, Moreover, the asymptotic normality is concluded for a large class of estimators of the extreme value index. These results are applied to stationary solutions of a general stochastic difference equation.