SOARS 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.