A New Regression-Based Tail Index Estimator

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 theory, and can potentially be applied in a very general context. 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 a. Second, it is relatively resilient to the choice of the tail length used in the estimation of a, and particularly so when compared to the widely used Hill estimator. Third, when the effect of the slowly varying part of the Pareto type model (the so called second order behavior of the Taylor expansion) vanishes slowly our estimator continues to perform satisfactorily, whereas the Hill estimator rapidly deteriorates.

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