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Tail Analysis Without Parametric Models: A Worst-Case Perspective


  • Henry Lam

    () (Department of Industrial Engineering and Operations Research, Columbia University, New York, New York 10027)

  • Clementine Mottet

    () (Department of Mathematics and Statistics, Boston University, Boston, Massachusetts 02215)


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.

Suggested Citation

  • Henry Lam & Clementine Mottet, 2017. "Tail Analysis Without Parametric Models: A Worst-Case Perspective," Operations Research, INFORMS, vol. 65(6), pages 1696-1711, December.
  • Handle: RePEc:inm:oropre:v:65:y:2017:i:6:p:1696-1711
    DOI: 10.1287/opre.2017.1643

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    1. Yuen, Robert & Stoev, Stilian & Cooley, Daniel, 2020. "Distributionally robust inference for extreme Value-at-Risk," Insurance: Mathematics and Economics, Elsevier, vol. 92(C), pages 70-89.
    2. Aleksandrina Goeva & Henry Lam & Huajie Qian & Bo Zhang, 2019. "Optimization-Based Calibration of Simulation Input Models," Operations Research, INFORMS, vol. 67(5), pages 1362-1382, September.

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