A method of moments estimator of tail dependence
(2007) , 30 pages
Files
ISBADP0722.pdf
Open Access - Adobe PDF
- 346.35 KB
Details
- Authors
- 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 semiparametric model in which the stable tail dependence function 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 estimators 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.
- Affiliations
Citations
Einmahl, J. H. J., Krajina, A., & Segers, J. (2007). A method of moments estimator of tail dependence (STAT Discussion Paper 0722). https://hdl.handle.net/2078.5/33150