On improved estimation of the extreme value index with the use of a shifted Hill’s estimator

The importance of the heavy-tail phenomenon, and as well as, limitations of methods used to detect and measure this phenomenon, are sustaining incessant progress in the area of extreme value index estimation (EVI). Therefore, the paper is devoted to illumi-nate possibility of making the Hill’s estimator to be shift-invariant, so that unintended mis-estimating of the EVI may be reduced. The paper confronts the original Hill’s approach with Aban and Meerschaert’s [2001] ideas, which are, in addition, adopted, and modified by the author. Thus, the three estimation approaches are compared, and their accuracy is assessed by a simulation study. It occurs that in the Pareto distribution case, the best estimates, amongst the considered, seem to be the ones proposed by the author and based on a proper choice of the sample shift. In general, the present study elucidates clear advantages of the shift-invariance approach over the original Hill’s estimator.