Weighted least-squares estimators of tail indices

We propose a class of weighted least-squares estimators for the tail index of a regularly varying upper tail of a distribution. Universal asymptotic normality of the estimators is established over the whole model. Asymptotic mean square errors of these and earlier estimators are compared within a submodel of regular variation, more general than Hall's model. We also discuss the choice of the optimal weights and the choice of the number of extreme order statistics to be used.