Estimator of the Pareto Index Based on Nonparametric Test

We study asymptotic properties of an estimator of the Pareto tail index, obtained by an inversion of a suitable nonparametric test of tails in the Hodges–Lehmann manner. The estimator is of semiparametric nature, involving an unknown slowly varying function; however, we do not impose any special condition on the latter function. The estimator is strongly consistent and asymptotically normal under mild conditions, with the standardization based on the asymptotic power of the test. Unless we impose some additional conditions on the model, the slowly varying function generally leads to an asymptotic bias. Possible improvements of the finite-sample properties of the estimator are discussed.