Joint versus marginal estimation for bivariate extremes
Joint versus marginal estimation for bivariate extremes
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发表时间：
1992
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通讯作者：
D. Shi;Richard L. Smith;S. Coles
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作者：
D. Shi;Richard L. Smith;S. Coles
二元极值分布包含两种类型的参数;定义边缘分布的参数，以及定义适当标准化变量之间依赖关系的参数。作为一种替代完全最大似然联合分布的基础上，我们考虑了“边际估计”的方法，其中的利润率和依赖参数分别估计。这种方法在计算上实现起来更简单，但可能效率低下。渐近结果允许量化的低效率。这些概念是相关的一大类家庭的多元分布，但详细的分析仅限于Gumbel的逻辑模型与Gumbel或广义极值利润率。
Bivariate extreme value distributions contain parameters of two types; those that define the marginal distributions, and parameters defining the dependence between suitably standardized variates. As an alternative to full maximum likelihood based on the joint distribution, we consider a "marginal estimation" method in which the margin and dependence parameters are estimated separately. This method is simpler to implement computationally, but may be inefficient. Asymptotic results allow the inefficiency to be quantified. The concepts are relevant to a large class of families of multivariate distributions, but the detailed analysis is restricted to Gumbel's logistic model with Gumbel or Generalized Extreme Value margins.