It is important to quantify and predict rare events that have huge societal effects. Existing works on analyzing such events mainly rely on either inflexible parametric models or nonparametric models that are subject to “the curse of dimensionality”. We propose a new semi-parametric approach based on the tail single-index model to better balance between the model flexibility and parsimony. The procedure involves three steps by first obtaining a √ n-estimator of the index parameter and then applying the local polynomial regression to estimate the intermediate conditional quantiles, which are then extrapolated to the tails to estimate the extreme conditional quantiles. We establish the asymptotic properties of the proposed estimators, and demonstrate through simulation and the analysis of the Los Angeles mortality and air pollution data that the proposed method is easy to compute and leads to more stable and accurate estimation than alternative methods.

中文翻译：

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基于尾单指标模型的极端分位数估计

量化和预测具有巨大社会影响的罕见事件非常重要。现有的分析此类事件的工作主要依赖于不灵活的参数模型或受“维度诅咒”影响的非参数模型。我们提出了一种新的基于尾部单指标模型的半参数方法，以更好地平衡模型的灵活性和简约性。该过程包括三个步骤，首先获得指数参数的 √ n 估计量，然后应用局部多项式回归来估计中间条件分位数，然后将其外推到尾部以估计极端条件分位数。我们建立了所提议的估计量的渐近性质，