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 - Statistics for near independence in multivariate extreme values.
AU - Ledford, Anthony W.
AU - Tawn, Jonathan A.
PY - 1996/3
Y1 - 1996/3
N2 - We propose a multivariate extreme value threshold model for joint tail estimation which overcomes the problems encountered with existing techniques when the variables are near independence. We examine inference under the model and develop tests for independence of extremes of the marginal variables, both when the thresholds are fixed, and when they increase with the sample size. Motivated by results obtained from this model, we give a new and widely applicable characterisation of dependence in the joint tail which includes existing models as special cases. A new parameter which governs the form of dependence is of fundamental importance to this characterisation. By estimating this parameter, we develop a diagnostic test which assesses the applicability of bivariate extreme value joint tail models. The methods are demonstrated through simulation and by analysing two previously published data sets.
AB - We propose a multivariate extreme value threshold model for joint tail estimation which overcomes the problems encountered with existing techniques when the variables are near independence. We examine inference under the model and develop tests for independence of extremes of the marginal variables, both when the thresholds are fixed, and when they increase with the sample size. Motivated by results obtained from this model, we give a new and widely applicable characterisation of dependence in the joint tail which includes existing models as special cases. A new parameter which governs the form of dependence is of fundamental importance to this characterisation. By estimating this parameter, we develop a diagnostic test which assesses the applicability of bivariate extreme value joint tail models. The methods are demonstrated through simulation and by analysing two previously published data sets.
KW - Asymptotic independence • Coefficient of tail dependence • Extreme value theory • Generalised Pareto distribution • Maximum likelihood • Multivariate extreme value distribution • Nonregular estimation • Poisson process • Threshold exceedance
U2 - 10.1093/biomet/83.1.169
DO - 10.1093/biomet/83.1.169
M3 - Journal article
VL - 83
SP - 169
EP - 187
JO - Biometrika
JF - Biometrika
SN - 1464-3510
IS - 1
ER -