Exceedance-based nonlinear regression of tail dependence

TL;DR

This paper introduces a flexible generalized additive modeling framework for covariate-dependent tail dependence estimation in multivariate extremes, applicable to environmental data, capturing asymptotic dependence and independence.

Contribution

It develops a novel exceedance-based nonlinear regression approach for tail dependence that handles covariate effects and distinguishes between dependence regimes.

Findings

Estimates show asymptotic independence across stations.

Tail dependence decreases with spatial distance.

Distinct patterns observed for different station types and years.

Abstract

The probability and structure of co-occurrences of extreme values in multivariate data may critically depend on auxiliary information provided by covariates. In this contribution, we develop a flexible generalized additive modeling framework based on high threshold exceedances for estimating covariate-dependent joint tail characteristics for regimes of asymptotic dependence and asymptotic independence. The framework is based on suitably defined marginal pretransformations and projections of the random vector along the directions of the unit simplex, which lead to convenient univariate representations of multivariate exceedances based on the exponential distribution. Good performance of our estimators of a nonparametrically designed influence of covariates on extremal coefficients and tail dependence coefficients are shown through a simulation study. We illustrate the usefulness of our modeling framework on a large dataset of nitrogen dioxide measurements recorded in France between 1999 and 2012, where we use the generalized additive framework for modeling marginal distributions and tail dependence in monthly maxima. Our results imply asymptotic independence of data observed at different stations, and we find that the estimated coefficients of tail dependence decrease as a function of spatial distance and show distinct patterns for different years and for different types of stations (traffic vs. background).