A diagnostic for selecting the threshold in extreme value analysis

A new approach is suggested for choosing the threshold when fitting the Hil l estimator of a tail exponent to extreme value data. Our method is based o n an easily computed diagnostic, which in turn is founded directly on the H ill estimator itself, 'symmetrized' to remove the effect of the tail expone nt but designed to emphasize biases in estimates of that exponent. The attr actions of the method are its accuracy, its simplicity and the generality w ith which it applies. This generality implies that the technique has somewh at different goals from more conventional approaches, which are designed to accommodate the minor component of a postulated two-component Pareto mixtu re. Our approach does not rely on the second component being Pareto distrib uted. Nevertheless, in the conventional setting it performs competitively w ith recently proposed methods, and in more general cases it achieves optima l rates of convergence. A by-product of our development is a very simple an d practicable exponential approximation to the distribution of the Hill est imator under departures from the Pareto distribution.