Uniqueness and global optimality of the maximum likelihood estimator for the generalized extreme value distribution

Journal Article · 18 August 2021 · Biometrika

DOI: https://doi.org/10.1093/biomet/asab043 · OSTI ID:1828573

Zhang, Likun ^[1]; Shaby, Benjamin A. ^[2]

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1. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
2. Colorado State Univ., Fort Collins, CO (United States)

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.

• Research Organization: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Biological and Environmental Research (BER)
• Grant/Contract Number: AC02-05CH11231
• OSTI ID: 1828573
• Journal Information: Biometrika, Journal Name: Biometrika Journal Issue: 3 Vol. 109; ISSN 0006-3444
• Publisher: Oxford University PressCopyright Statement
• Country of Publication: United States
• Language: English