On the second order property of elliptical multivariate regular variation

Multivariate regular variation is a popular framework of multivariate extreme value analysis.However, a suitable parametric model needs to be introduced for efficient estimation of its spectral measure.In such a view, elliptical distributions have been employed for deriving such models.On the other hand, the second order behavior of multivariate regular variation has to be specified for investigating the property of the estimator.This paper derives such a behavior by imposing a widely adopted second order regular variation condition on the representation of elliptical distributions.As result, the second order variation for the convergence to spectral measure is characterized by a signed measure with a regular varying index.Moreover, it leads to the asymptotic bias of the estimator.For demonstration, multivariate t-distribution is considered.