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.Comment: 23 pages, 2 table
