ABSTRACT
Hidden Regular Variation
Krishanu Maulik, April 2, 2003
Asymptotic independence is used extensively in finance, data
network analysis and environmental statistics. Roughly speaking, the idea of
asymptotic independence means that a large value in one component is
unlikely to be accompanied by large values in other components. However, the
class of asymptotic independence is too broad a class. For example, jointly
normal random variables, which are not perfectly correlated, are
asymptotically independent. So we need a closer and deeper look at the
concept of the asymptotic independence. Hidden regular variation was defined
by Resnick (2002) as a semi-parametric subfamily of the family of
distributions possessing multivariate regular variation and asymptotic
independence. We shall discuss the concept of hidden regular variation in
details along with some other parametric refinements of asymptotic
independence.
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Igor Grubisic
(grubisic@math.uu.nl)