Research projects

Project CEMAPRE internal

TitleRegression-Based Tail Index Estimator
ParticipantsJoão Nicolau (Principal Investigator), Paulo Rodrigues
SummaryWe want to develop a new regression-based approach for the estimation of the tail index of
heavy-tailed distributions. Comparatively to many procedures currently available in the literature,
our method does not involve order statistics and can be applied in more general contexts than just
Pareto. The procedure is in line with approaches used in experimental data analysis with fixed
explanatory variables, and has several important features which are worth highlighting. First, it
provides a bias reduction when compared to 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. Fourth, our estimator
performs well under dependence of unknown form. For inference purposes, we also provide a way to
compute the asymptotic variance of the proposed estimator under these general conditions (e.g. time
dependence and conditional heteroscedasticity).