论文标题
极端的部分尾巴相关
Partial Tail Correlation for Extremes
论文作者
论文摘要
为了了解极端变量集之间的结构关系，我们发展了一个与部分相关的极端类似物。我们首先开发由独立规则变化随机变量的转换线性组合构建的内部产品空间。我们通过内部产品空间的投影定理定义部分尾巴相关。我们表明，部分尾巴相关可以理解为转换线性预测的预测错误的内部产物。我们将部分尾部相关连接到内部产物矩阵的倒数，并表明该反向的零意味着零的部分尾相关。然后，我们表明，在建模假设下，随机变量属于内部产品空间的明智子集，内部产物的矩阵对应于先前研究的尾部成对依赖矩阵。我们为零的部分尾部相关性开发了假设检验。我们在两种应用中演示了表现：华盛顿特区的高氮二氧化氮水平和上层多瑙河盆地的极端河流排放。
In order to understand structural relationships among sets of variables at extreme levels, we develop an extremes analogue to partial correlation. We begin by developing an inner product space constructed from transformed-linear combinations of independent regularly varying random variables. We define partial tail correlation via the projection theorem for the inner product space. We show that the partial tail correlation can be understood as the inner product of the prediction errors from transformed-linear prediction. We connect partial tail correlation to the inverse of the inner product matrix and show that a zero in this inverse implies a partial tail correlation of zero. We then show that under a modeling assumption that the random variables belong to a sensible subset of the inner product space, the matrix of inner products corresponds to the previously-studied tail pairwise dependence matrix. We develop a hypothesis test for partial tail correlation of zero. We demonstrate the performance in two applications: high nitrogen dioxide levels in Washington DC and extreme river discharges in the upper Danube basin.
