  The extremal dependence structure of a regularly varying random vector Xis
fully described by its limiting spectral measure. In this paper, we investigate
how torecover characteristics of the measure, such as extremal coefficients,
from the extremalbehaviour of convex combinations of components of X. Our
considerations result in aclass of new estimators of moments of the
corresponding combinations for the spectralvector. We show asymptotic normality
by means of a functional limit theorem and, focusingon the estimation of
extremal coefficients, we verify that the minimal asymptoticvariance can be
achieved by a plug-in estimator using subsampling bootstrap. We illustratethe
benefits of our approach on simulated and real data.
