Propagation of Input Tail Uncertainty in Rare-Event Estimation: A Light versus Heavy Tail Dichotomy
arxiv(2023)
摘要
We consider the estimation of small probabilities or other risk quantities
associated with rare but catastrophic events. In the model-based literature,
much of the focus has been devoted to efficient Monte Carlo computation or
analytical approximation assuming the model is accurately specified. In this
paper, we study a distinct direction on the propagation of model uncertainty
and how it impacts the reliability of rare-event estimates. Specifically, we
consider the basic setup of the exceedance of i.i.d. sum, and investigate how
the lack of tail information of each input summand can affect the output
probability. We argue that heavy-tailed problems are much more vulnerable to
input uncertainty than light-tailed problems, reasoned through their large
deviations behaviors and numerical evidence. We also investigate some
approaches to quantify model errors in this problem using a combination of the
bootstrap and extreme value theory, showing some positive outcomes but also
uncovering some statistical challenges.
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