Varying Index Coefficient Model for Tail Index Regression

Hongyu An and Boping Tian ()
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Hongyu An: School of Mathematics, Harbin Institute of Technology, Xidazhi, Harbin 150001, China
Boping Tian: School of Mathematics, Harbin Institute of Technology, Xidazhi, Harbin 150001, China

Mathematics, 2024, vol. 12, issue 13, 1-35

Abstract: Investigating the causes of extreme events is crucial across various fields. However, existing asymptotic theoretical models often lack flexibility and fail to capture the complex dependency structures inherent in extreme events. Additionally, the scarcity of extreme event data and the challenge of fully nonparametric estimation with high-dimensional covariates lead to the “curse of dimensionality”, complicating the analysis of extreme events. Considering the nonlinear interactions among covariates, we propose a flexible model that combines varying index coefficient models with extreme value theory to address these issues. This approach effectively avoids the curse of dimensionality while providing robust explanatory power and high flexibility. Our model also includes a variable selection process, for which we have demonstrated the consistency of the estimators and the oracle property of the variable selection. Monte Carlo simulation results validate the finite sample properties of the estimators. Furthermore, an empirical analysis of tail risk in financial markets offers valuable insights into the drivers of risk.

Keywords: BSBK; extreme value theory; oracle property; Pareto-type tail distribution; varying index coefficient model; variable selection (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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