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Statistics for near independence in multivariate extreme values.

Ledford, Anthony W. and Tawn, Jonathan A. (1996) Statistics for near independence in multivariate extreme values. Biometrika, 83 (1). pp. 169-187. ISSN 1464-3510

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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.

Item Type: Article
Journal or Publication Title: Biometrika
Uncontrolled Keywords: Asymptotic independence • Coefficient of tail dependence • Extreme value theory • Generalised Pareto distribution • Maximum likelihood • Multivariate extreme value distribution • Nonregular estimation • Poisson process • Threshold exceedance
Subjects: Q Science > QA Mathematics
Departments: Faculty of Science and Technology > Mathematics and Statistics
ID Code: 19548
Deposited By: ep_ss_importer
Deposited On: 11 Nov 2008 11:51
Refereed?: Yes
Published?: Published
Last Modified: 09 Oct 2013 15:40
Identification Number:
URI: http://eprints.lancs.ac.uk/id/eprint/19548

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