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Γενικό Σεμινάριο Μαθηματικών

  • Στοιχεία επικοινωνίαςΑ. Κοτσιώλης, Καθηγητήςemail:cotsioli AT math.upatras.gr

05.11.2008, Αίθουσα 342 κτίριο Βιολογίας/Μαθηματικών

Ημερομηνία:  Τετάρτη 5  Νοεμβρίου  2008

Τόπος:  Αίθουσα 342 κτίριο Βιολογίας/Μαθηματικών

Ώρα:  13:00 – 14:00 μ.μ.

Ομιλητής: Αριστείδης Νικολουλόπουλος

                   Διδάκτορας Τμήματος Στατιστικής

                  του Οικονομικού Πανεπιστημίου Αθηνών

Θέμα : Dependence modelling and construction of multivariate copulas

Περίληψη

There are two goals for constructing multivariate copulas for dependence modelling. For continuous data there is a need for copulas with a flexible range of lower/upper tail dependence, while for discrete data for copulas with a wide range of dependence, including negative dependence. In this talk we will define such copulas. Firstly, exploiting the use of finite mixture of simple uncorrelated normal distributions we will define a copula suitable for modelling multivariate discrete data. Since the correlation vanishes, the cumulative distribution is simply the product of univariate normal cumulative distribution functions, while the mixing operation introduces dependence. Hence we obtain a kind of flexible dependence, and allow for negative dependence. Secondly, introducing the multivariate tail dependence functions we will derive the extreme value copulas of t-copulas, called the t-EV copulas. As two special cases, the Hüsler-Reiss and the Marshall-Olkin distributions emerge as limits of the t-EV copula as the degrees of freedom go to infinity and zero respectively. The t copula and its extremal variants attain a wide range in the set of bivariate tail dependence parameters. Finally, the extremal dependence of vines copulas will be examined exploiting the use of tail dependence functions. By choosing bivariate copulas appropriately, vine copulas can have a flexible range of bivariate lower and upper tail dependence parameters, and different upper/lower tail dependence for each bivariate margin; the latter property is not provided by multivariate t copulas.

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