Rapid variation with remainder and rates of convergence

J. Beirlant, E. Willekens
1990 Advances in Applied Probability  
In this paper, we refine the concept of Γ-variation up to second order, and we give a characterization of this type of asymptotic behaviour. We apply our results to obtain uniform rates of convergence in the weak convergence of renormalised sample maxima to the double exponential distribution. In a second application we derive a rate of convergence result for the Hill estimator.
doi:10.1017/s0001867800023132 fatcat:k6dr67f5vjdo3nxgvhstsdigje