Statistics of heteroscedastic extremes

• 成果类型: Article
• 署名作者: Einmahl, John H. J.; de Haan, Laurens; Zhou, Chen
• 署名单位: Tilburg University; Erasmus University Rotterdam - Excl Erasmus MC; Erasmus University Rotterdam; Universidade de Lisboa; European Central Bank; De Nederlandsche Bank NV
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12099
• 发表日期: 2016
• 页码: 31-51
• 关键词: tail index; models

摘要

We extend classical extreme value theory to non-identically distributed observations. When the tails of the distribution are proportional much of extreme value statistics remains valid. The proportionality function for the tails can be estimated non-parametrically along with the (common) extreme value index. For a positive extreme value index, joint asymptotic normality of both estimators is shown; they are asymptotically independent. We also establish asymptotic normality of a forecasted high quantile and develop tests for the proportionality function and for the validity of the model. We show through simulations the good performance of the procedures and also present an application to stock market returns. A main tool is the weak convergence of a weighted sequential tail empirical process.