Authors: Bücher, Axel
Segers, Johan
Title: On the maximum likelihood estimator for the generalized extreme-value distribution
Language (ISO): en
Abstract: The vanilla method in univariate extreme-value theory consists of fitting the three-parameter Generalized Extreme-Value (GEV) distribution to a sample of block maxima. Despite claims to the contrary, the asymptotic normality of the maximum likelihood estimator has never been established. In this paper, a formal proof is given using a general result on the maximum likelihood estimator for parametric families that are differentiable in quadratic mean but whose support depends on the parameter. An interesting side result concerns the (lack of) differentiability in quadratic mean of the GEV family.
Subject Headings: differentiability in quadratic mean
Lipschitz condition
generalized extreme-value distribution
Fisher information
empirical process
maximum likelihood
Issue Date: 2016
Appears in Collections:Sonderforschungsbereich (SFB) 823

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