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

被引：38
|
作者：
Buecher, Axel [1 ]
Segers, Johan [2 ]
机构：
[1] Ruhr Univ Bochum, Fak Math, Univ Str 150, D-44780 Bochum, Germany
[2] Catholic Univ Louvain, Inst Stat Biostat & Sci Actuarielles, Voie Roman Pays 20, B-1348 Louvain, Belgium
来源：
EXTREMES | 2017年 / 20卷 / 04期
关键词：
Differentiability in quadratic mean; M-estimator; Maximum likelihood; Empirical process; Fisher information; Generalized Extreme-Value distribution; Lipschitz condition; Support; FREQUENCY-DISTRIBUTION; VALUE INDEX; PARAMETERS;
D O I：
10.1007/s10687-017-0292-6
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
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页码：839 / 872
页数：34
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