IMPROVED INFERENCE ON RISK MEASURES FOR UNIVARIATE EXTREMES

• 成果类型: Article
• 署名作者: Belzile, Leo R.; Davison, Anthony C.
• 署名单位: Universite de Montreal; HEC Montreal; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
• 刊物名称: ANNALS OF APPLIED STATISTICS
• ISSN/ISSBN: 1932-6157
• DOI: 10.1214/21-AOAS1555
• 发表日期: 2022
• 页码: 1524-1549
• 关键词: MAXIMUM-LIKELIHOOD ESTIMATORS; bias reduction; parameters; posterior; BAYES; tail

摘要

We discuss the use of likelihood asymptotics for inference on risk measures in univariate extreme value problems, focusing on estimation of high quantiles and similar summaries of risk for uncertainty quantification. We study whether higher-order approximation, based on the tangent exponential model, can provide improved inferences. We conclude that inference based on maxima is generally robust to mild model misspecification and that profile likelihood-based confidence intervals will often be adequate, whereas inferences based on threshold exceedances can be badly biased but may be improved by higher-order methods, at least for moderate sample sizes. We use the methods to shed light on catastrophic rainfall in Venezuela, flooding in Venice, and the lifetimes of Italian semisupercentenarians.