ABSTRACT
Abstract The main objective of statistics of extremes is the prediction of rare events, and its primary problem has been the estimation of the extreme value index (EVI). When we are interested in large values, estimation is usually performed on the basis of the largest k + 1 order statistics in the sample or on the excesses over a high level u. A question that has been often addressed in practical applications of extreme value theory is the choice of either k or u, and an adaptive EVI-estimation. The choice can be either heuristic or based on sample path stability or on the minimization of a mean square error estimate as a function of k. Some of these procedures will be reviewed. All these methods can be applied, with adequate modifications, not only to the adaptive EVI-estimation but also to the adaptive estimation of other relevant right tail parameters. We shall illustrate the methods essentially for a positive EVI.
