An utopic adventure in the modelling of conditional univariate and multivariate extremes

Abstract

The EVA 2023 data competition consisted of four challenges, ranging from interval estimation for very high quantiles of univariate extremes conditional on covariates, point estimation of unconditional return levels under a custom loss function, to estimation of the probabilities of tail events for low and high-dimensional multivariate data. We tackle these tasks by revisiting the current and existing literature on conditional univariate and multivariate extremes. We propose new cross-validation methods for covariate-dependent models, validation metrics for exchangeable multivariate models, formulae for the joint probability of exceedance for multivariate generalized Pareto vectors and a composition sampling algorithm for generating multivariate tail events for the latter. We highlight overarching themes ranging from model validation at extremely high quantile levels to building custom estimation strategies that leverage model assumptions.

arXiv comment42 pages, 9 figures, 10 tables

References in corpus (9)

• MissForest - nonparametric missing value imputation for mixed-type data
• Smoothing parameter and model selection for general smooth models
• Fast calibrated additive quantile regression
• Cross-validatory extreme value threshold selection and uncertainty with application to ocean storm severity
• A new representation for multivariate tail probabilities
• Posterior propriety in Bayesian extreme value analyses using reference priors
• Detection of Block-Exchangeable Structure in Large-Scale Correlation Matrices
• Hypothesis tests for structured rank correlation matrices
• Simultaneous computation of Kendall's tau and its jackknife variance