Abstract
Original language  English 

Qualification  Doctor of Philosophy 
Awarding Institution 

Supervisors/Advisors 

Award date  23 Apr 2010 
Place of Publication  Tilburg 
Publisher  
Print ISBNs  9789056682521 
Publication status  Published  2010 
Fingerprint
Cite this
}
An Mestimator of multivariate tail dependence. / Krajina, A.
Tilburg : Universiteit van Tilburg, 2010. 99 p.Research output: Thesis › Phd Thesis 4 Research NOT TU/e / Graduation NOT TU/e)
TY  THES
T1  An Mestimator of multivariate tail dependence
AU  Krajina, A.
PY  2010
Y1  2010
N2  Extreme value theory is the part of probability and statistics that provides the theoretical background for modeling events that almost never happen. The estimation of the dependence between two or more such unlikely events (tail dependence) is the topic of this thesis. The tail dependence structure is modeled by the stable tail dependence function. In Chapter 2 a semiparametric model is considered in which the stable tail dependence function is parametrically modeled. A method of moments estimator of the unknown parameter is proposed, where an integral of a nonparametric, rankbased estimator of the stable tail dependence function is matched with the corresponding parametric version. This estimator is applied in Chapter 3 to estimate the tail dependence structure of the family of metaelliptical distributions. The estimator introduced in Chapter 2 is extended in two respects in Chapter 4: (i) the number of variables is arbitrary; (ii) the number of moment equations can exceed the dimension of the parameter space. This estimator is defined as the value of the parameter vector that minimizes the distance between a vector of weighted integrals of the tail dependence function on the one hand and empirical counterparts of these integrals on the other hand. The method, not being likelihood based, applies to discrete and continuous models alike. Under minimal conditions all estimators introduced are consistent and asymptotically normal. The performance and applicability of the estimators is demonstrated by examples.
AB  Extreme value theory is the part of probability and statistics that provides the theoretical background for modeling events that almost never happen. The estimation of the dependence between two or more such unlikely events (tail dependence) is the topic of this thesis. The tail dependence structure is modeled by the stable tail dependence function. In Chapter 2 a semiparametric model is considered in which the stable tail dependence function is parametrically modeled. A method of moments estimator of the unknown parameter is proposed, where an integral of a nonparametric, rankbased estimator of the stable tail dependence function is matched with the corresponding parametric version. This estimator is applied in Chapter 3 to estimate the tail dependence structure of the family of metaelliptical distributions. The estimator introduced in Chapter 2 is extended in two respects in Chapter 4: (i) the number of variables is arbitrary; (ii) the number of moment equations can exceed the dimension of the parameter space. This estimator is defined as the value of the parameter vector that minimizes the distance between a vector of weighted integrals of the tail dependence function on the one hand and empirical counterparts of these integrals on the other hand. The method, not being likelihood based, applies to discrete and continuous models alike. Under minimal conditions all estimators introduced are consistent and asymptotically normal. The performance and applicability of the estimators is demonstrated by examples.
UR  http://repository.uvt.nl/id/iruvtnl:oai:wo.uvt.nl:3969610
M3  Phd Thesis 4 Research NOT TU/e / Graduation NOT TU/e)
SN  9789056682521
PB  Universiteit van Tilburg
CY  Tilburg
ER 