Extrapolation of extreme covariates in generalized additive regression using extreme-value theory
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.