2020/08/14 by Likun Zhang, Zhang, Likun, Benjamin A. Shaby +2 · 2 citations
Economics, Econometrics and Finance · Mathematics · #FOS: Computer and information sciences #FOS: Mathematics #Financial Risk and Volatility Modeling #Methodology (stat.ME) #Statistical Distribution Estimation and Applications #Statistical Methods and Inference #Statistics Theory (math.ST) #math.ST #stat.ME #stat.TH
paper · pdf · doi:10.48550/arxiv.2008.06400
38 pages, 5 figures
arxiv created 2020/08/14 · openalex publication_date 2020/08/14 · arxiv updated 2020/08/17 · openalex created_date 2020/08/21 · openalex updated_date 2026/07/28
The three-parameter generalized extreme value distribution arises from classical univariate extreme value theory and is in common use for analyzing the far tail of observed phenomena. Curiously, important asymptotic properties of likelihood-based estimation under this standard model have yet to be established. In this paper, we formally 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 neighborhood of the shape parameter.