Tail Analysis Without Parametric Models: A Worst-Case Perspective
针对尾部数据稀缺导致参数模型选择困难的问题，提出基于尾部凸性几何假设的最坏情况边界计算方法，通过低维非线性规划区分极端轻尾或重尾行为，数值实验表明该方法比传统参数方法更可靠。
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/opre.2017.1643 .