Computer-intensive rate estimation, diverging statistics and scanning

• 成果类型: Article
• 署名作者: Mcelroy, Tucker; Politis, Dimitris N.
• 署名单位: University of California System; University of California San Diego
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053607000000064
• 发表日期: 2007
• 页码: 1827-1848
• 关键词: tail index; long memory; CONVERGENCE

摘要

A general rate estimation method is proposed that is based on studying the in-sample evolution of appropriately chosen diverging/converging statistics. The proposed rate estimators are based on simple least squares arguments, and are shown to be accurate in a very general setting without requiring the choice of a tuning parameter. The notion of scanning is introduced with the purpose of extracting useful subsamples of the data series; the proposed rate estimation method is applied to different scans, and the resulting estimators are then combined to improve accuracy. Applications to heavy tail index estimation as well as to the problem of estimating the long memory parameter are discussed; a small simulation study complements our theoretical results.