Citation

Ledford ANTHONYW, Tawn JONATHANA. Biometrika 1996; 83(1): 169-187.

Copyright

(Copyright © 1996, Biometrika Trust, Publisher Oxford University Press)

DOI

10.1093/biomet/83.1.169

PMID

unavailable

Abstract

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.