On the maximum likelihood estimator for the Generalized Extreme-Value distribution

By Axel Bucher, Johan Segers. Extremes, 2016

86 citations recorded by the source corpus.

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 supports depend on the parameter. An interesting side result concerns the (lack of) differentiability in quadratic mean of the GEV family.

Subfields: Finance, Global and Planetary Change, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/420f829a9f03cc1ae6006b0d07c78339dddb9a56

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Citations in the corpus

Maximum likelihood estimators based on the block maxima method (2017, methodology): “[16], Smith [22], Bücher and Segers [4]).”
A Horse Race between the Block Maxima Method and the Peak–over–Threshold Approach (2018, background): “Perhaps surprisingly, asymptotic theory for the BM method has hitherto mostly ignored the fact that block maxima are only approximately GEV distributed (see, e.g., Prescott and Walden, 1980; Hosking, Wallis and Wood, 1985; Bücher and Segers, 2017, among others).”