A method of moments estimator of tail dependence
(2008) Bernoulli : a journal of mathematical statistics and probability — Vol. 14, n° 4, p. 1003-1026 (2008)
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- Abstract
- In the world of multivariate extremes, estimation of the dependence structure still presents a challenge and an interesting problem. A procedure for the bivariate case is presented that opens the road to a similar way of handling the problem in a truly multivariate setting. We consider a semi-parametric model in which the stable tail dependence Junction is parametrically modeled. Given a random sample from a bivariate distribution function, the problem is to estimate the unknown parameter. A method of moments estimator is proposed where a certain integral of a nonparametric, rank-based estimator of the stable tail dependence function is matched with the corresponding parametric version. Under very weak conditions, the estimator is shown to be consistent and asymptotically normal. Moreover, a comparison between the parametric and nonparametric estimator,, leads to a goodness-of-fit test for the semiparametric model. The performance of the estimator is illustrated for a discrete spectral measure that arises in a factor-type model and for which likelihood-based methods break down. A second example is that of a family of stable tail dependence functions of certain meta-elliptical distributions.
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Einmahl, J. H. J., Krajina, A., & Segers, J. (2008). A method of moments estimator of tail dependence. Bernoulli : a journal of mathematical statistics and probability, 14(4), 1003-1026. https://doi.org/10.3150/08-BEJ130 (Original work published 2008)