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Journal of Data Science


EVIboost for the Estimation of Extreme Value Index Under Heterogeneous Extremes
Volume 21, Issue 4 (2023), pp. 638–657
Pub. online: 3 October 2022      Type: Statistical Data Science      Open accessOpen Access
Received
18 June 2022
Accepted
16 September 2022
Published
3 October 2022

Abstract

Modeling heterogeneity on heavy-tailed distributions under a regression framework is challenging, yet classical statistical methodologies usually place conditions on the distribution models to facilitate the learning procedure. However, these conditions will likely overlook the complex dependence structure between the heaviness of tails and the covariates. Moreover, data sparsity on tail regions makes the inference method less stable, leading to biased estimates for extreme-related quantities. This paper proposes a gradient boosting algorithm to estimate a functional extreme value index with heterogeneous extremes. Our proposed algorithm is a data-driven procedure capturing complex and dynamic structures in tail distributions. We also conduct extensive simulation studies to show the prediction accuracy of the proposed algorithm. In addition, we apply our method to a real-world data set to illustrate the state-dependent and time-varying properties of heavy-tail phenomena in the financial industry.

Supplementary material

 Supplementary Material
The following files are included in the supplementary material: (1) Programs for modeling TIR and EVIboost; (2) Code files for simulation study, along with the detailed experiment results; (3) Code and data files for financial data analysis via EVIboost; (4) Simulation results on computational time of the EVIboost model.

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Copyright
2023 The Author(s). Published by the School of Statistics and the Center for Applied Statistics, Renmin University of China.
Open access article under the CC BY license.

Keywords
gradient boosting heterogeneous extremes Pareto model tail estimation tree-based method

Funding
Yanxi Hou’s research was partly supported by the National Natural Science Foundation of China Grant 72171055 and the Natural Science Foundation of Shanghai Grant 20ZR1403900.

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