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Uniqueness and global optimality of the maximum likelihood estimator for the generalized extreme value distribution
- Source :
- Biometrika, vol 109, iss 3
- Publication Year :
- 2021
- Publisher :
- eScholarship, University of California, 2021.
-
Abstract
- 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.<br />38 pages, 5 figures
- Subjects :
- FOS: Computer and information sciences
Statistics and Probability
General Mathematics
Statistics & Probability
Mathematics - Statistics Theory
Statistics Theory (math.ST)
Law of large numbers
Shape parameter
Methodology (stat.ME)
Consistency (statistics)
FOS: Mathematics
Applied mathematics
Limit (mathematics)
Uniqueness
Econometrics
Extreme value theory
Statistics - Methodology
Standard model (cryptography)
Mathematics
Profile likelihood
Numerical and Computational Mathematics
Block maximum
Applied Mathematics
Statistics
Univariate
Global maximum
Agricultural and Biological Sciences (miscellaneous)
Convergence rate
Generalized extreme value distribution
Support
Statistics, Probability and Uncertainty
General Agricultural and Biological Sciences
Subjects
Details
- Database :
- OpenAIRE
- Journal :
- Biometrika, vol 109, iss 3
- Accession number :
- edsair.doi.dedup.....22a44837ae298d6a163c4795f5782360