INFERENCE FOR THE LIMITING CLUSTER SIZE DISTRIBUTION OF EXTREME VALUES

• 成果类型: Article
• 署名作者: Robert, Christian Y.
• 署名单位: heSam Universite; Conservatoire National Arts & Metiers (CNAM)
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/07-AOS551
• 发表日期: 2009
• 页码: 271-310
• 关键词: poisson random sums; stationary sequence; Empirical Processes; index estimation; dependent data; BEHAVIOR

摘要

Any limiting point process for the time normalized exceedances of high levels by a stationary sequence is necessarily compound Poisson under appropriate long range dependence conditions. Typically exceedances appear in clusters. The underlying Poisson points represent the cluster positions and the multiplicities correspond to the cluster sizes. In the present paper we introduce estimators of the limiting Cluster size probabilities, which are constructed through a recursive algorithm. We derive estimators of the extremal index which plays a key role in determining the intensity of cluster positions. We study the asymptotic properties of the estimators and investigate their finite sample behavior on simulated data.