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

On the occurrence times of componentwise maxima and bias in likelihood inference for multivariate max-stable distributions