Nonparametric estimation of multivariate extreme-value copulas
(2012)
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- Authors
- Supervisors
- Segers, Johan
- Abstract
- (en) Extreme-value copulas arise in the asymptotic theory for componentwise maxima of independent random samples and are determined by the so-called Pickands dependence function. In this thesis, the focus lies on the nonparametric estimation of multivariate extreme-value copulas. In a first project, the hypothetical situation is considered where the marginal distributions are supposed to be known. The existing nonparametric estima- tors require the choice of weight functions, of which we succeed to compute the variance-minimizing versions together with an estimator for the Pickands depen- dence function based on ordinary least squares in a linear regression framework. The following chapters of the thesis are dedicated to the more realistic situ- ation of unknown marginal distributions which are replaced by their empirical counterparts. As the shape constraints for the Pickands dependence function are in general not satisfied by the nonparametric estimators referred to above, we will enforce the constraints by replacing the initial estimator by its best least-squares approximation in the set of Pickands dependence functions having a discrete spectral measure supported on a sufficiently fine grid. The last chapter presents a new test for multivariate extreme-value depen- dence based on the Pickands representation and implemented using the multi- plier resampling method. 1G
- Affiliations
Citations
Gudendorf, G. (2012). Nonparametric estimation of multivariate extreme-value copulas. https://hdl.handle.net/2078.5/160395