  Full likelihood-based inference for high-dimensional multivariate extreme
value distributions, or max-stable processes, is feasible when incorporating
occurrence times of the maxima; without this information, $d$-dimensional
likelihood inference is usually precluded due to the large number of terms in
the likelihood. However, some studies have noted bias when performing
high-dimensional inference that incorporates such event information,
particularly when dependence is weak. We elucidate this phenomenon, showing
that for unbiased inference in moderate dimensions, dimension $d$ should be of
a magnitude smaller than the square root of the number of vectors over which
one takes the componentwise maximum. A bias reduction technique is suggested
and illustrated on the extreme value logistic model.
