A Heuristic Procedure to Estimate the Tail Index

The estimation of the tail index is a very important issue within extreme value theory. Semi-parametric estimators usually require the choice of the number k of upper order statistics to use in the estimation, which is a difficult problem to handle. Here it is applied a heuristic graphical method to well-known semi-parametric tail index estimators and analyze it through simulation. It will be seen that some criteria lead to good results.