论文标题
条件模型的极端特征
Extremal Characteristics of Conditional Models
论文作者
论文摘要
有条件指定的模型通常用于描述复杂的多元数据。这样的模型在极端上采用隐式结构。到目前为止，尚无方法来计算条件模型的极端特征，因为副群和边缘没有以封闭形式表达。我们考虑指定$ x $的分布以及$ y $的分布在$ x $上的双变量条件模型。我们提供工具来量化有关此类模型极端的隐式假设。特别是，这些工具使我们能够近似$ y $的尾巴的分布以及以封闭形式的渐近独立性$η$的系数。我们将这些方法应用于波高和波周期的广泛使用的条件模型。此外，我们引入了Heffernan和Tawn（2004）条件极端模型的参数空间的新条件，并证明有条件的极端模型不会捕获$η$，当$η<1 $。
Conditionally specified models are often used to describe complex multivariate data. Such models assume implicit structures on the extremes. So far, no methodology exists for calculating extremal characteristics of conditional models since the copula and marginals are not expressed in closed forms. We consider bivariate conditional models that specify the distribution of $X$ and the distribution of $Y$ conditional on $X$. We provide tools to quantify implicit assumptions on the extremes of this class of models. In particular, these tools allow us to approximate the distribution of the tail of $Y$ and the coefficient of asymptotic independence $η$ in closed forms. We apply these methods to a widely used conditional model for wave height and wave period. Moreover, we introduce a new condition on the parameter space for the conditional extremes model of Heffernan and Tawn (2004), and prove that the conditional extremes model does not capture $η$, when $η<1$.
