A Method of Moments Estimator of Tail Dependence in Elliptical Copula Models

An elliptical copula model is a distribution function whose copula is that of an elliptical distri- bution. The tail dependence function in such a bivariate model has a parametric representation with two parameters: a tail parameter and a correlation parameter. The correlation parameter can be estimated by robust methods based on the whole sample. Using the estimated correla- tion parameter as plug-in estimator, we then estimate the tail parameter applying a modification of the method of moments approach proposed in the paper by J.H.J. Einmahl, A. Krajina and J. Segers [Bernoulli 14(4), 2008, 1003-1026]. We show that such an estimator is consistent and asymptotically normal. Also, we derive the joint limit distribution of the estimators of the two parameters. By a simulation study, we illustrate the small sample behavior of the estimator of the tail parameter and we compare its performance to that of the estimator proposed in the paper by C. KlÄuppelberg, G. Kuhn and L. Peng [Scandinavian Journal of Statistics 35(4), 2008, 701-718].asymptotic normality;elliptical copula;elliptical distribution;meta-elliptical model;method of moments;semi-parametric model;tail dependence

An M-Estimator for Tail Dependence in Arbitrary Dimensions

Consider a random sample in the max-domain of attraction of a multivariate extreme value distribution such that the dependence structure of the attractor belongs to a parametric model. A new estimator for the unknown parameter is defined as the value that minimises the distance between a vector of weighted integrals of the tail dependence function and their empirical counterparts. The minimisation problem has, with probability tending to one, a unique, global solution. The estimator is consistent and asymptotically normal. The spectral measures of the tail dependence models to which the method applies can be discrete or continuous. Examples demonstrate the applicability and the performance of the method.asymptotic statistics;factor model;M-estimation;multivariate extremes;tail dependence

Estimating Extreme Bivariate Quantile Regions

AMS 2000 subject classifications. Primary 62G32, 62G05; secondary 60G70, 60F05.

An M-estimator of multivariate tail dependence.

AN M-ESTIMATOR OF TAIL DEPENDENCE. 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, rank-based 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 meta-elliptical 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.

Cardiovascular care of patients with stroke and high risk of stroke: The need for interdisciplinary action: A consensus report from the European Society of Cardiology Cardiovascular Round Table.

Comprehensive stroke care is an interdisciplinary challenge. Close collaboration of cardiologists and stroke physicians is critical to ensure optimum utilisation of short- and long-term care and preventive measures in patients with stroke. Risk factor management is an important strategy that requires cardiologic involvement for primary and secondary stroke prevention. Treatment of stroke generally is led by stroke physicians, yet cardiologists need to be integrated care providers in stroke units to address all cardiovascular aspects of acute stroke care, including arrhythmia management, blood pressure control, elevated levels of cardiac troponins, valvular disease/endocarditis, and the general management of cardiovascular comorbidities. Despite substantial progress in stroke research and clinical care has been achieved, relevant gaps in clinical evidence remain and cause uncertainties in best practice for treatment and prevention of stroke. The Cardiovascular Round Table of the European Society of Cardiology together with the European Society of Cardiology Council on Stroke in cooperation with the European Stroke Organisation and partners from related scientific societies, regulatory authorities and industry conveyed a two-day workshop to discuss current and emerging concepts and apparent gaps in stroke care, including risk factor management, acute diagnostics, treatments and complications, and operational/logistic issues for health care systems and integrated networks. Joint initiatives of cardiologists and stroke physicians are needed in research and clinical care to target unresolved interdisciplinary problems and to promote the best possible outcomes for patients with stroke