On the maximum likelihood estimator for the Generalized Extreme-Value distribution
On the maximum likelihood estimator for the Generalized Extreme-Value distribution
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DOI：
10.1007/s10687-017-0292-6
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发表时间：
2017-12-01
期刊：
影响因子：
1.3
通讯作者：
Segers, Johan
中科院分区：
文献类型：
--
作者：
Buecher, Axel;Segers, Johan
单变量极值理论中的香草方法包括将三参数广义极值（GEV）分布拟合到块极大值的样本。尽管有相反的说法，但最大似然估计量的渐近正态性从未建立。本文利用一个一般结果给出了支持度依赖于参数的二次均值可微的参数族的极大似然估计的一个形式证明。一个有趣的副作用是关于GEV族的二次均值的可微性（缺乏）。
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.