The classical approach to analyzing extreme value data is the generalized Pareto distribution (GPD). When the GPD is used to explain a target variable with the large dimension of covariates, the shape and scale function of covariates included in GPD are sometimes modeled using the generalized additive models (GAM). In contrast to many results of application, there are no theoretical results on the hybrid technique of GAM and GPD, which motivates us to develop its asymptotic theory. We provide the rate of convergence of the estimator of shape and scale functions, as well as its local asymptotic normality.

翻译：分析极值数据的经典方法是广义帕累托分布(GPD)。当GPD用于解释具有高维协变量的目标变量时，GPD中包含的协变量的形状函数和尺度函数有时会使用广义可加模型(GAM)进行建模。与众多应用结果相比，关于GAM与GPD混合技术的理论结果尚属空白，这促使我们发展其渐近理论。我们给出了形状函数和尺度函数估计量的收敛速度，以及其局部渐近正态性。