Weighted approximations to tail copula processes with application to testing the extreme value condition

By John H. J. Einmahl, Laurens de Haan, Deyuan Li. 2006

63 citations recorded by the source corpus.

Consider $n$ i.i.d. random vectors on $\mathbb{R}^2$, with unknown, common distribution function $F$. Under a sharpening of the extreme value condition on $F$, we derive a weighted approximation of the corresponding tail copula process. Then we construct a test to check whether the extreme value condition holds by comparing two estimators of the limiting extreme value distribution, one obtained from the tail copula process and the other obtained by first estimating the spectral measure which is then used as a building block for the limiting extreme value distribution. We derive the limiting distribution of the test statistic from the aforementioned weighted approximation. This limiting distribution contains unknown functional parameters. Therefore, we show that a version with estimated parameters converges weakly to the true limiting distribution. Based on this result, the finite sample properties of our testing procedure are investigated through a simulation study. A real data application is also presented.

Subfields: Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/e0f8bed98f47048d2bd314ca03959e05a7933b21

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Citations in the corpus

Extreme-value copulas (2009, background): “See for instance [5, 13, 49, 24, 59, 60, 61, 63] for some (semi-)parametric approaches and [1, 6, 23, 22, 25, 81] for some nonparametric ones.”
A method of moments estimator of tail dependence (2007, methodology): “defined in [ 6 ] and [5, 11], respectively; here k ∈ {1,...,n}.”
Maximum Empirical Likelihood Estimation of the Spectral Measure of an Extreme Value Distribution (2008, background): “As the new estimator takes values in the class of spectral measures, it can be easily transformed into estimators for the aforementioned other objects that can be used to describe the dependence structure of G. This holds in particular for the Pickands (1981) dependence function and the stable tail ”
Estimation of the marginal expected shortfall: the mean when a related variable is extreme (2012, unknown): “It follows from, for instance, a modiﬁcation of Example 1.8 in Alexander (1986) or that of Lemma 3.2 in Einmahl et al. (2006).”