  This paper addresses important weaknesses in current methodology for the
estimation of multivariate extreme event distributions. The estimation of the
residual dependence index $\eta \in (0,1]$ is notoriously problematic. We
introduce a flexible class of reduced-bias estimators for this parameter,
designed to ameliorate the usual problems of threshold selection through a
unified approach to the familiar margins standardisation. We derive the
associated asymptotic properties. The efficacy of the proposed semi-parametric
inference on $\eta$ stems from a hitherto neglected exponentially decaying term
in the hidden regular variation characterisation. Simulation studies to assess
the performance for finite samples over a range of standard copulas indicate an
improved performance, relative to the existing standard methods such as the
Hill estimator. Our leading application illustrates how asymptotic independence
can be discerned from monsoon-related rainfall occurrences at different
locations in Ghana. The considerations involved in extending this framework to
feasible inference on the extreme value index attached to domains of attraction
are briefly discussed.
