A new approach to extreme value theory is presented for vector data with heavy tails. The tail index is allowed to vary with direction, where the directions are not necessarily along the coordinate axes. Basic asymptotic theory is developed, using operator regular variation and extremal integrals. A test is proposed to judge whether the tail index varies with direction in any given data set.

中文翻译：

---

具有操作员规范的极值理论。

针对重尾向量数据提出了一种极值理论的新方法。尾部索引允许随方向变化，其中方向不一定沿着坐标轴。使用算子正则变分和极值积分开发了基本的渐近理论。提出了一个测试来判断任何给定数据集中的尾部索引是否随方向变化。