On the distribution of tail array sums for strongly mixing stationary sequences

• 成果类型: Article
• 署名作者: Rootzen, H; Leadbetter, MR; de Haan, L
• 署名单位: Chalmers University of Technology; University of North Carolina; University of North Carolina Chapel Hill; Erasmus University Rotterdam - Excl Erasmus MC; Erasmus University Rotterdam
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• 发表日期: 1998
• 页码: 868-885
• 关键词: index estimation; dependent data

摘要

This paper concerns the asymptotic distributions of tail array sums of the form Sigma psi(n)(X-i - u(n)) where {X-i} is a strongly mixing stationary sequence, psi(n) are real functions which are constant for negative arguments, psi(n)(x) = psi(n)(X+) and {u(n)} are levels with u(n) --> infinity. Compound Poisson limits for rapid convergence of u(n) --> infinity (nP{X-1 > u(n)} --> tau < infinity) are considered briefly and a more detailed account given for normal limits applicable to slower rates (nP(X-1 > u(n)) --> infinity). The work is motivated by (1) the modeling of damage due to very high and moderately high extremes and (2) the provision of probabilistic theory for application to problems of tail inference for stationary sequences.