A sum characterization of hidden regular variation in joint tail modeling with likelihood inference via the MCEM algorithm

01/18/2013 - 12:00pm
Mesa Laboratory, Chapman Room

Grant Weller, CSU Fort Collins

A fundamental deficiency of classical multivariate extreme value theory is the inability to distinguish between asymptotic independence and exact independence.  In this work, we examine multivariate threshold modeling based on the framework of regular variation on cones.  Tail dependence is described by a limiting measure, which in some cases is degenerate on joint tail regions despite strong sub-asymptotic dependence in such regions.  The canonical example is a bivariate Gaussian distribution with any correlation less than one. Hidden regular variation, a higher-order tail decay on these regions, offers a refinement of the classical theory. This work develops a representation of random vectors possessing hidden regular variation as the sum of independent regular varying components. The representation is shown to be asymptotically valid via a multivariate tail equivalence result, and is demonstrated via simulation on the bivariate Gaussian example.  We develop a likelihood-based estimation procedure from this representation via a version of the Monte Carlo EM algorithm which has been modified for tail estimation.  The methodology is demonstrated on simulated data and applied to a bivariate series of air pollution data from Leeds, UK. We demonstrate the improvement in tail risk estimates offered by the sum representation over approaches which ignore hidden regular variation in the data.

Date: Friday, January 18, 2013 - 12:00pm

Location: Mesa Laboratory, Chapman Room