  Inference over tails is performed by applying only the results of extreme
value theory. Whilst such theory is well defined and flexible enough in the
univariate case, multivariate inferential methods often require the imposition
of arbitrary constraints not fully justifed by the underlying theory. In
contrast, our approach uses only the constraints imposed by theory. We build on
previous, theoretically justified work for marginal exceedances over a high,
unknown threshold, by combining it with flexible, semiparametric copulae
specifications to investigate extreme dependence. Whilst giving probabilistic
judgements about the extreme regime of all marginal variables, our approach
formally uses the full dataset and allows for a variety of patterns of
dependence, be them extremal or not. A new probabilistic criterion quantifying
the possibility that the data exhibits asymptotic independence is introduced
and its robustness empirically studied. Estimation of functions of interest in
extreme value analyses is performed via MCMC algorithms. Attention is also
devoted to the prediction of new extreme observations. Our approach is
evaluated through a series of simulations, applied to real data sets and
assessed against competing approaches. Evidence demonstrates that the bulk of
the data does not bias and improves the inferential process for the extremal
dependence.
