|An Alternative Representation of Hidden Regular Variation in Multivariate Extremes
Grant Weller, Department of Statistics, Colorado State University
Thursday, May 18, 2012
In this work in progress, we propose an alternative characterization for a multivariate regular varying random vector with hidden regular variation. Regular variation on cones provides a useful framework for describing dependence in the upper tail of a multivariate distribution. Tail dependence can be described by a limiting angular measure on the unit sphere; however, in many cases, the angular measure places zero mass on some regions of the sphere. The canonical example is a bivariate Gaussian random vector with any correlation less than one; in this case the angular measure degenerates to point masses on the endpoints and thus fails to capture the hidden dependence at sub-asymptotic levels.