2ND-ORDER REGULAR VARIATION, CONVOLUTION AND THE CENTRAL-LIMIT-THEOREM

Second-order regular variation is a refinement of the concept of regul ar variation which is useful for studying rates of convergence in extr eme value theory and asymptotic normality of tail estimators, For a di stribution tail 1 - F which possesses second-order regular variation, we discuss how this property is inherited by 1 - F-2 and 1 - F-2. We also discuss the relationship of central limit behavior of tail empiri cal processes, asymptotic normality of Hill's estimator and second-ord er regular variation. (C) 1997 Elsevier Science B.V.