From scarcity to insight: extreme events analysis with a partially linear single-index varying-coefficient model in high-dimensional settings

Analysing the causes of extreme events holds paramount importance across diverse domains. However, conventional models with asymptotic theory often exhibit limitations in flexibly capturing the intricate dependence structure in extreme events. Additionally, the scarcity of data on extreme events further complicates the nonparametric estimation of high-dimensional covariates, giving rise to the challenge known as the ‘dimensional curse.’ In order to address these challenges, we propose a flexible model that combines a partially linear single-index varying-coefficient model with extreme value theory, and it effectively avoids the curse of dimensionality while providing a strong interpretative ability and high flexibility. Consistency and oracle properties of estimators are established. The Monte Carlo simulation results confirm the finite sample properties of the estimators. Furthermore, the application to a real-world example involving network analysis of sector index risk in financial markets and valuable insights into risk drivers are obtained.