Identifying groups of variables with the potential of being large simultaneously

TL;DR

This paper develops a nonparametric, rank-based method to identify groups of variables with potential for large simultaneous values by analyzing joint tail dependence, using a systematic search algorithm with a novel stopping criterion.

Contribution

It introduces a new algorithm for detecting tail-dependent variable groups using asymptotic distributions of rank-based estimators and a conditional tail dependence coefficient to improve stopping criteria.

Findings

Algorithm effectively detects tail-dependent groups.

Hill-type estimator enhances detection accuracy.

Method outperforms existing approaches in numerical experiments.

Abstract

Identifying groups of variables that may be large simultaneously amounts to finding out which joint tail dependence coefficients of a multivariate distribution are positive. The asymptotic distribution of a vector of nonparametric, rank-based estimators of these coefficients justifies a stopping criterion in an algorithm that searches the collection of all possible groups of variables in a systematic way, from smaller groups to larger ones. The issue that the tolerance level in the stopping criterion should depend on the size of the groups is circumvented by the use of a conditional tail dependence coefficient. Alternatively, such stopping criteria can be based on limit distributions of rank-based estimators of the coefficient of tail dependence, quantifying the speed of decay of joint survival functions. Numerical experiments indicate that the algorithm's effectiveness for detecting tail-dependent groups of variables is highest when paired with a criterion based on a Hill-type estimator of the coefficient of tail dependence.