Linear combinations of order statistics to estimate the position and scale parameters of the Generalized Extreme Values distribution

 Ad hoc techniques for estimating the position and the scale parameters of the Generalized Extreme Values distribution are introduced. The estimators proposed are simple linear combinations of the order statistics: they provide valuable estimates of the parameters of interest both when the shape parameter is known and when it is unknown (this latter case being of great relevance in practical applications), and show a good performance as well when the sample size is small. In addition, weakly-consistent estimators of the position parameter are introduced, whose calculation does not require the knowledge of any of the remaining parameters. The procedures are tested on simulated data, and comparisons with other techniques are shown.