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Regression-type analysis for multivariate extreme values.

Miguel de Carvalho1, Alina Kumukova2, Gonçalo Dos Reis1,3

  • 1School of Mathematics, University of Edinburgh, Edinburgh, UK.

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Summary
This summary is machine-generated.

This study introduces a new regression model for extreme values, accounting for multivariate extreme value distributions and extreme value copulas. The model offers insights into financial market risks, particularly extreme losses.

Keywords:
Angular measureBernstein polynomialsExtreme value copulaJoint extremesMultivariate extreme value distributionQuantile regressionStatistics of extremes

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Area of Science:

  • Statistics
  • Extreme Value Theory
  • Econometrics

Background:

  • Standard regression models often fail with extreme data.
  • Extreme value theory is crucial for understanding rare events.
  • Multivariate extreme value distributions capture dependencies in extreme data.

Purpose of the Study:

  • To develop a novel regression model for situations with extreme responses and covariates.
  • To incorporate extreme value copulas into a regression framework.
  • To analyze the conditional risk of extreme losses in financial markets.

Main Methods:

  • A regression-type model is devised for multivariate extreme value data.
  • The model leverages extreme value copulas, unlike standard methods.
  • Bernstein polynomial priors are used on angular densities for model learning.

Main Results:

  • Numerical studies indicate strong performance of the proposed methods.
  • The framework identifies a regression manifold based on asymptotic results.
  • Analysis of financial data reveals insights into extreme loss risks.

Conclusions:

  • The proposed model effectively handles extreme response and covariate data.
  • The approach provides a robust framework for analyzing extreme value dependencies.
  • The findings have implications for understanding and managing financial risks.