Tail Analysis Without Parametric Models: A Worst-Case Perspective
Tail Analysis Without Parametric Models: A Worst-Case Perspective
复制标题
没有参数模型的尾部分析：最坏情况的视角
DOI：
--
复制
发表时间：
2015
影响因子：
2.7
通讯作者：
Clementine Mottet
中科院分区：
文献类型：
--
作者：
H. Lam;Clementine Mottet
评估极值性能指标的一个常见瓶颈是，由于其本身的性质，尾部数据通常非常有限。传统方法使用参数拟合从尾部数据中选择最佳概率分布，但参数选择的有效性可能难以验证。本文介绍了一种替代的基础上计算的最坏情况下的边界的几何前提下的尾部凸性，所有常见的参数尾部分布的特征。我们刻画了优化问题的最优性结构，并证明了最坏情况下的凸尾行为在某种意义上是极轻尾或极重尾。我们开发了低维非线性程序，区分这两种情况，并计算最坏情况下的界限。我们数值说明所提出的方法可以提供更可靠的性能比传统的参数方法。在线附录可在https://doi.org/10.1287/.
A common bottleneck in evaluating extremal performance measures is that, because of their very nature, tail data are often very limited. The conventional approach selects the best probability distribution from tail data using parametric fitting, but the validity of the parametric choice can be difficult to verify. This paper describes an alternative based on the computation of worst-case bounds under the geometric premise of tail convexity, a feature shared by all common parametric tail distributions. We characterize the optimality structure of the resulting optimization problem, and demonstrate that the worst-case convex tail behavior is in a sense either extremely light tailed or extremely heavy tailed. We develop low-dimensional nonlinear programs that distinguish between the two cases and compute the worst-case bound. We numerically illustrate how the proposed approach can give more reliable performances than conventional parametric methods. The online appendix is available at https://doi.org/10.1287/...
影响因子：
4.5
作者：
Seregin,Arseni;Wellner,JonA
通讯作者：
Wellner,JonA