Uniqueness and global optimality of the maximum likelihood estimator for the generalized extreme value distribution
成果类型：
Article
署名作者：
Zhang, Likun; Shaby, Benjamin A.
署名单位：
United States Department of Energy (DOE); Lawrence Berkeley National Laboratory; Colorado State University System; Colorado State University Fort Collins
刊物名称：
BIOMETRIKA
ISSN/ISSBN：
0006-3444
DOI：
10.1093/biomet/asab043
发表日期：
2022
页码：
853864
关键词：
摘要：
The three-parameter generalized extreme value distribution arises from classical univariate extreme value theory, and is in common use for analysing the far tail of observed phenomena, yet important asymptotic properties of likelihood-based estimation under this standard model have not been established. In this paper we prove that the maximum likelihood estimator is global and unique. An interesting secondary result entails the uniform consistency of a class of limit relations in a tight neighbourhood of the true shape parameter.