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

Wadsworth, Jennifer (2015) On the occurrence times of componentwise maxima and bias in likelihood inference for multivariate max-stable distributions. Biometrika, 102 (3). pp. 705-711. ISSN 0006-3444

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Abstract

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, ddd-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 ddd 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.