Second-order regular variation, convolution and the central limit theorem

Second-order regular variation is a refinement of the concept of regular variation which is useful for studying rates of convergence in extreme value theory and asymptotic normality of tail estimators. For a distribution tail 1 − F which possesses second-order regular variation, we discuss how this property is inherited by 1 − F2 and 1 − F∗2. We also discuss the relationship of central limit behavior of tail empirical processes, asymptotic normality of Hillʹs estimator and second-order regular variation.