A New Regression-Based Tail Index Estimator

Resumo/Abstract: In this paper, a new regression-based approach for the estimation of the tail index of heavy-tailed distributions is introduced. Comparatively to many procedures currently available in the literature, our method does not involve order statistics, and can be applied in more general contexts. The procedure is in line with approaches used in experimental data analysis with fixed explanatory variables. There are several important features of our procedure worth highlighting. First, it provides a bias reduction over available regression-based methods and a fortiori over standard least-squares based estimators of the tail index.
Second, it is more resilient to the choice of the tail length used in the estimation of the index than the widely used Hill estimator. Third, when the effect of the slowly varying function at infinity of the Pareto distribution (the so called second order behavior of the Taylor
expansion) vanishes slowly our estimator continues to perform satisfactorily, whereas the Hill estimator rapidly deteriorates.

Outros seminários / Other seminars: Programa completo / Full programme.