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

[摘要] 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 - F-2 and 1 - F-*2. We also discuss the relationship of central limit behavior of tail empirical processes, asymptotic normality of Hill's estimator and second-order regular variation. (C) 1997 Elsevier Science B.V.

[发布日期] 1997-09-01

[关键词] regular variation;second-order behavior;tail empirical measure;extreme value theory;convolution;maxima;Hill estimator