arXiv:2606.14268v1 Announce Type: cross Abstract: We develop a statistical learning theory for gradient boosting applied to the estimation of covariate-dependent Generalized Pareto (GP) distributions in the context of Peaks-over-Threshold modeling. After an orthogonal reparametrization of the GP likelihood that diagonalizes its Fisher information matrix, we cast the estimation problem within the Empirical Risk Minimization (ERM) framework and derive non-asymptotic error bounds for the boosting estimator. Our analysis accounts for three distinct sources of error in the process: statistical fluc
The continuous advancement in statistical learning theory and the increasing complexity of real-world datasets, particularly in risk-sensitive sectors like insurance, drive the need for more robust and accurate predictive models.
This development offers a more principled and theoretically sound approach to extreme value modeling, improving risk assessment and financial stability for critical industries.
The application of gradient boosting to Generalized Pareto distributions provides a more rigorous statistical framework for predicting rare events, potentially leading to more accurate insurance pricing and capital allocation.
- · Insurance companies
- · Financial risk modelers
- · Academic researchers in machine learning
- · Actuaries
- · Traditional extreme value theory methods
- · Less statistically robust machine learning approaches
Improved accuracy in predicting high-impact, low-frequency events in financial and environmental domains.
Potential for new insurance products and risk transfer mechanisms based on more reliable extreme event modeling.
Enhanced resilience of financial systems against black swan events through better probabilistic forecasting.
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