On second order conditions in the multivariate block maxima and peak over threshold method
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Date
2018
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Abstract
Second order conditions provide a natural framework for establishing asymptotic
results about estimators for tail related quantities. Such conditions are typically
tailored to the estimation principle at hand, and may be vastly different for estimators
based on the block maxima (BM) method or the peak-over-threshold (POT)
approach. In this paper we provide details on the relationship between typical second
order conditions for BM and POT methods in the multivariate case. We show that the
two conditions typically imply each other, but with a possibly different second order
parameter. The latter implies that, depending on the data generating process, one
of the two methods can attain faster convergence rates than the other. The class of
multivariate Archimax copulas is examined in detail; we find that this class contains
models for which the second order parameter is smaller for the BM method and vice
versa. The theory is illustrated by a small simulation study.
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Keywords
domain of attraction, extremal dependence, madogram, extreme value statistics, Pickands dependence function, archimax copulas