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

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Likun Zhang and Benjamin A Shaby

Biometrika, 2022, vol. 109, issue 3, 853-864

Abstract: SummaryThe 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.

Keywords: Block maximum, Convergence rate, Global maximum, Law of large numbers, Profile likelihood; Support (search for similar items in EconPapers)
Date: 2022
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