We introduce a novel regression model for the conditional left and right tail of a possibly heavy-tailed response. The proposed model can be used to learn the effect of covariates on an extreme value setting via a Lasso-type specification based on a Lagrangian restriction. Our model can be used to track if some covariates are significant for the lower values, but not for the (right) tail—and vice versa; in addition to this, the proposed model bypasses the need for conditional threshold selection in an extreme value theory framework. We assess the finite-sample performance of the proposed methods through a simulation study that reveals that our method recovers the true conditional distribution over a variety of simulation scenarios, along with being accurate on variable selection. Rainfall data are used to showcase how the proposed method can learn to distinguish between key drivers of moderate rainfall, against those of extreme rainfall. Supplementary materials accompanying this paper appear online.

我们为可能重尾响应的条件左尾和右尾引入了一种新的回归模型。所提出的模型可用于通过基于拉格朗日约束的套索类型规范来学习协变量对极值设置的影响。我们的模型可用于跟踪某些协变量是否对较低值显着，但对（右）尾部不显着，反之亦然；除此之外，所提出的模型绕过了极值理论框架中条件阈值选择的需要。我们通过模拟研究评估了所提出方法的有限样本性能，该研究表明我们的方法在各种模拟场景中恢复了真实的条件分布，同时在变量选择上是准确的。降雨数据用于展示所提出的方法如何学会区分中等降雨和极端降雨的关键驱动因素。本文随附的补充材料出现在网上。