Existence and consistency of the maximum likelihood estimators for the extreme value index within the block maxima framework
Existence and consistency of the maximum likelihood estimators for the extreme value index within the block maxima framework
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DOI：
10.3150/13-bej573
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发表时间：
2015-02-01
期刊：
影响因子：
1.5
通讯作者：
Dombry, Clement
中科院分区：
文献类型：
--
作者：
Dombry, Clement
最大似然法提供了一种标准的方法来估计广义极值（GEV）分布的三个参数。它与块极大值法相结合，在实际应用中常用来求满足一阶极值条件的分布的极值指标和归一化常数，并隐含地假定块极大值是GEV分布。这是不令人满意的，因为GEV分布仅对于大尺寸的块是块最大值分布的良好近似。本文旨在为这一方法论提供理论基础。仅在一阶极值条件下，在块极大值方法的框架下，证明了极值指标和归一化常数的极大似然估计的存在性和相合性.
The maximum likelihood method offers a standard way to estimate the three parameters of a generalized extreme value (GEV) distribution. Combined with the block maxima method, it is often used in practice to assess the extreme value index and normalization constants of a distribution satisfying a first order extreme value condition, assuming implicitly that the block maxima are exactly GEV distributed. This is unsatisfactory since the GEV distribution is a good approximation of the block maxima distribution only for blocks of large size. The purpose of this paper is to provide a theoretical basis for this methodology. Under a first order extreme value condition only, we prove the existence and consistency of the maximum likelihood estimators for the extreme value index and normalization constants within the framework of the block maxima method.