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NEW DOCTORAL DEGREE An M-Estimator of Multivariate Tail Dependence
Andrea Krajina
; Tilburg University, Tilburg, The Netherlands
Abstract
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.
Keywords
Hrčak ID:
53697
URI
Publication date:
10.6.2010.
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