Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Dependence properties of multivariate max-stable distributions
AU - Papastathopoulos, Ioannis
AU - Tawn, Jonathan
PY - 2014/9
Y1 - 2014/9
N2 - For an m-dimensional multivariate extreme value distribution there exist 2m−1 exponent measures which are linked and completely characterise the dependence of the distribution and all of its lower dimensional margins. In this paper we generalise the inequalities of Schlather and Tawn (2002) for the sets of extremal coefficients and construct bounds that higher order exponent measures need to satisfy to be consistent with lower order exponent measures. Subsequently we construct nonparametric estimators of the exponent measures which impose, through a likelihood-based procedure, the new dependence constraints and provide an improvement on the unconstrained estimators.
AB - For an m-dimensional multivariate extreme value distribution there exist 2m−1 exponent measures which are linked and completely characterise the dependence of the distribution and all of its lower dimensional margins. In this paper we generalise the inequalities of Schlather and Tawn (2002) for the sets of extremal coefficients and construct bounds that higher order exponent measures need to satisfy to be consistent with lower order exponent measures. Subsequently we construct nonparametric estimators of the exponent measures which impose, through a likelihood-based procedure, the new dependence constraints and provide an improvement on the unconstrained estimators.
KW - Max-stable distributions
KW - Multivariate extremes
KW - Exponent measure
KW - Inequalities
KW - Constrained estimators
U2 - 10.1016/j.jmva.2014.05.001
DO - 10.1016/j.jmva.2014.05.001
M3 - Journal article
VL - 130
SP - 134
EP - 140
JO - Journal of Multivariate Analysis
JF - Journal of Multivariate Analysis
SN - 0047-259X
ER -