On the maximum likelihood estimator for the Generalized Extreme-Value distribution
Statistics Theory
2017-03-16 v3 Statistics Theory
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 supports depend on the parameter. An interesting side result concerns the (lack of) differentiability in quadratic mean of the GEV family.
Cite
@article{arxiv.1601.05702,
title = {On the maximum likelihood estimator for the Generalized Extreme-Value distribution},
author = {Axel Bücher and Johan Segers},
journal= {arXiv preprint arXiv:1601.05702},
year = {2017}
}
Comments
31 pages, 1 figure