使用极值理论在广义加性回归中对极端协变量进行外推
Extrapolation of extreme covariates in generalized additive regression using extreme-value theory
- INRAE（法国国家农业食品环境研究院）
- University of Geneva（日内瓦大学）
- Univ Brest, CNRS UMR 6205, Laboratoire de Mathématiques de Bretagne Atlantique（布雷斯特大学、法国国家科学研究中心第6205联合研究单位、布列塔尼大西洋数学实验室）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
研究在协变量外推时提升广义加性模型预测性能的方法，将GAMs与多元极值理论渐近模型结合，考虑二元及连续响应，以欧洲野火应用为例探索新方法对预测的改善。
AI中文摘要：
我们提出了在协变量外推的背景下提高广义加性模型（GAMs）预测性能的方法，此时预测依赖于超出其观测范围的协变量。使用诸如GAMs等预测模型时，训练和预测数据集之间的协变量分布可能会发生变化。忽略此问题可能导致协变量分布尾部的预测不准确。例如，在气候变化情景中此问题尤为关键，因为从未来气候情景模拟的协变量可能包含更多极端情况。我们的方法将协变量分布主体的GAMs与高协变量值下多元极值理论的渐近模型相结合。我们考虑基于潜在变量假设的二元响应以及连续响应。对于协变量的大值，在由极值理论激发的特定边际尺度上，当使用适当的链接函数时，潜在变量或连续响应被假设为线性依赖于带有加性误差项的协变量。在欧洲野火的应用中，我们使用环境和气象协变量探索新方法如何改善预测。
英文摘要：
Predictions with covariates in the tails of the covariate distribution often lack accuracy and are highly uncertain but may be of critical importance in many applications. New covariates may even lie beyond the range of training data. The problem can be particularly critical in environmental contexts, for example with climate-change scenarios, where new covariates represent future, more extreme climate conditions. We here propose novel methods to improve generalized additive models (GAMs) with focus on extreme covariates and covariate extrapolation. Adopting a random-design setting, we continuously integrate GAMs for the bulk of covariate distributions with models motivated by multivariate extreme value theory for high covariate values. We consider continuous responses but develop also a new approach for binary responses by assuming a continuous latent response variable. Our framework imposes a specific structure for large values of the covariates motivated by extreme value theory: by combining a transformation to a specific marginal scale with an appropriate link function, the continuous response variable depends linearly on the covariates. In an application to occurrences and sizes of large wildfires in Europe for the period 2008-2023, we explore how the new method can improve predictions, especially during extreme conditions, using environmental and meteorological covariates.
