On the Maximum Likelihood Estimator for the Generalized Extreme-Value Distribution

Bücher, Axel;Segers, Johan
(2016) , 29 pages

Files

ISBADP2016_03_segers_OntheMaximumLikelihoodEstimator_dial.pdf
  • Open Access
  • Adobe PDF
  • 509.02 KB
Download

Details

Authors
  • Bücher, AxelDortmund University, Germany
    Author
  • Segers, JohanUCLouvain
    Author
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.
Affiliations

Citations

  • APA
  • Chicago
  • FWB

Bücher, A., & Segers, J. (2016). On the Maximum Likelihood Estimator for the Generalized Extreme-Value Distribution (ISBA Discussion Paper 2016/03). https://hdl.handle.net/2078.5/184569