Bücher, AxelSegers, Johan2016-01-262016-01-262016http://hdl.handle.net/2003/3447010.17877/DE290R-16526The 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.enDiscussion Paper / SFB 823;3/2016differentiability in quadratic meansupportLipschitz conditiongeneralized extreme-value distributionFisher informationempirical processmaximum likelihoodM-estimator310330620working paper