Nonparametric estimation of the spectral measure, and associated dependence measures, for multivariate extreme values using a limiting conditional representation.

Eastoe, Emma F. and Heffernan, Janet E. and Tawn, Jonathan A. (2014) Nonparametric estimation of the spectral measure, and associated dependence measures, for multivariate extreme values using a limiting conditional representation. Extremes, 17 (1). pp. 25-43. ISSN 1386-1999

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Abstract

The traditional approach to multivariate extreme values has been through the multivariate extreme value distribution G, characterised by its spectral measure H and associated Pickands’ dependence function A. More generally, for all asymptotically dependent variables, H determines the probability of all multivariate extreme events. When the variables are asymptotically dependent and under the assumption of unit Fréchet margins, several methods exist for the estimation of G, H and A which use variables with radial component exceeding some high threshold. For each of these characteristics, we propose new asymptotically consistent nonparametric estimators which arise from Heffernan and Tawn’s approach to multivariate extremes that conditions on variables with marginal values exceeding some high marginal threshold. The proposed estimators improve on existing estimators in three ways. First, under asymptotic dependence, they give self-consistent estimators of G, H and A; existing estimators are not self-consistent. Second, these existing estimators focus on the bivariate case, whereas our estimators extend easily to describe dependence in the multivariate case. Finally, for asymptotically independent cases, our estimators can model the level of asymptotic independence; whereas existing estimators for the spectral measure treat the variables as either being independent, or asymptotically dependent. For asymptotically dependent bivariate random variables, the new estimators are found to compare favourably with existing estimators, particularly for weak dependence. The method is illustrated with an application to finance data.

Item Type:
Journal Article
Journal or Publication Title:
Extremes
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2200/2201
Subjects:
?? asymptotic dependenceconditional distribution economic monetary unionmultivariate extreme value theory nonparametric modellingpoisson processengineering (miscellaneous)economics, econometrics and finance (miscellaneous)statistics and probabilityqa mathema ??
ID Code:
69423
Deposited By:
Deposited On:
09 May 2014 23:01
Refereed?:
Yes
Published?:
Published
Last Modified:
15 Jul 2024 10:30