Non-crossing neural network quantile regression estimation for driving data with telematics

• Xenxo Vidal-Llana ^[1] ; Carlos Salort Sánchez ^[1] ; Vincenzo Coia ^[3] ; Montserrat Guillén ^[2]
  1. [1] Universitat de València

     Universitat de València

     Valencia, España

     
  2. [2] Universitat de Barcelona

     Universitat de Barcelona

     Barcelona, España

     
  3. [3] BGC Engineering Inc., Vancouver, BC Canada

  Mostrar afiliaciones +
• Localización: Sort: Statistics and Operations Research Transactions, ISSN 1696-2281, Vol. 50, Nº. 1, 2026, págs. 43-66
• Idioma: inglés
• Enlaces
  • Texto completo (pdf)
• Resumen

  • State-of-the-art methods for estimating extreme quantiles (value at risk, VaR) and their tail expectations (conditional tail expectation, CTE) under covariate control primarily rely on quantile regression but lack explicit constraints for non-crossing conditions. To address this, we introduce the non-crossing dual neural network, a deep learning model that simultaneously estimates VaRs and CTEs across multiple quantile levels, incorporates covariate dependence, and enables the reconstruction of individual conditional distributions and risk profiles while ensuring the natural order of quantile levels. Using a 2015 telematics dataset, the proposed methodology outperforms benchmark models while enforcing previously unaddressed conditions. The model can be used to identify risk within an insurance portfolio and to analyze extreme right-tail behaviour at the individual level.