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Second order conditions provide a natural framework for establishingasymptotic results about estimators for tail related quantities. Suchconditions are typically tailored to the estimation principle at hand, and maybe vastly different for estimators based on the block maxima (BM) method or thepeak-over-threshold (POT) approach. In this paper we provide details on therelationship between typical second order conditions for BM and POT methods inthe multivariate case. We show that the two conditions typically imply eachother, but with a possibly different second order parameter. The latter impliesthat, depending on the data generating process, one of the two methods canattain faster convergence rates than the other. The class of multivariateArchimax copulas is examined in detail; we find that this class contains modelsfor which the second order parameter is smaller for the BM method and viceversa. The theory is illustrated by a small simulation study.

On Second Order Conditions in the Multivariate Block Maxima and Peak over Threshold Method