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<p>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 generalized additive models (GAM). In contrast to many results of applications, no theoretical results have been reported for 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.</p>

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Asymptotic Theory for Extreme Value Generalized Additive Model

  • 期刊论文

  • 发表日期：

    2025年12月2日

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  • Takuma Yoshida

摘要

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 generalized additive models (GAM). In contrast to many results of applications, no theoretical results have been reported for 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.