Threshold selection is a fundamental problem in any threshold-based extreme value analysis. While models are asymptotically motivated, selecting an appropriate threshold for finite samples can be difficult through standard methods. Inference can also be highly sensitive to the choice of threshold. Too low a threshold choice leads to bias in the fit of the extreme value model, while too high a choice leads to unnecessary additional uncertainty in the estimation of model parameters. In this paper, we develop a novel methodology for automated threshold selection that directly tackles this bias-variance trade-off. We also develop a method to account for the uncertainty in this threshold choice and propagate this uncertainty through to high quantile inference. Through a simulation study, we demonstrate the effectiveness of our method for threshold selection and subsequent extreme quantile estimation. We apply our method to the well-known, troublesome example of the River Nidd dataset.

翻译：阈值选择是基于阈值的极值分析中的基本问题。尽管模型在渐近意义上具有理论支撑，但通过标准方法为有限样本选择合适阈值往往存在困难，且推断结果对阈值选择高度敏感。阈值过低会导致极值模型拟合产生偏差，而阈值过高则会在模型参数估计中引入不必要的额外不确定性。本文提出了一种直接解决这一偏差-方差权衡问题的自动阈值选择新方法，同时开发了量化阈值选择不确定性的技术，并将此不确定性传播至高分位数推断过程。通过模拟研究，我们验证了该方法在阈值选择及后续极值分位数估计中的有效性，并将其应用于著名的尼德河数据集这一棘手实例。