TAIL INDEX ESTIMATION, PARETO QUANTILE PLOTS, AND REGRESSION DIAGNOSTICS

Successful application of extreme value statistics for estimating the Pareto tail index relies heavily on the choice of the number of extrem e values taken into account. It is shown that these tail index estimat ors can be considered estimates of the slope at the right upper tail o f a Pareto quantile plot, obtained using a weighted least squares algo rithm. From this viewpoint, based on classical ideas on regression dia gnostics, algorithms can be constructed searching for that order stati stic to the right of which one obtains an optimal linear fit of the qu antile plot.