Statistics of extremes by oracle estimation

• 成果类型: Article
• 署名作者: Grama, Ion; Spokoiny, Vladimir
• 署名单位: Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/07-AOS535
• 发表日期: 2008
• 页码: 1619-1648
• 关键词: regular variation; sample fraction; parameters; index; CONVERGENCE; bootstrap; rates

摘要

We use the fitted Pareto law to construct an accompanying approximation of the excess distribution function. A selection rule of the location of the excess distribution function is proposed based on a stagewise lack-of-fit testing procedure. Our main result is an oracle type inequality for the Kullback-Leibler loss.