Abstract. Consider a distribution $F$ with regularly varying tails of index $\alpha$. An estimation strategy for $\alpha$, exploiting the relation between the behavior of the tail at infinity and that of the characteristic function near the origin is proposed. A semi-parametric regression model does the job: a non-parametric component controls the bias and a parametric one produces the actual estimate. Implementation of the estimation strategy is quite simple as it can rely on standard software packages for generalized additive models. A generalized cross validation procedure is suggested in order to handle the bias-variance trade-off. The theoretical properties of the proposed procedure, consistency and asymptotic normality, are derived. Simulations show the excellent performance of this estimator in a wide range of cases. An application to data sets on city sizes, facing the debated issue of distinguishing Pareto-type tails from Log-normal tails, illustrates how the proposed method works in practice.

Key words: heavy-tailed distributions, regular variation, empirical characteristic function, Zipf’s law.

Speaker: prof. Emanuele Taufer

The seminar will be held on Wednesday 31 January 2018 at 14:00 at the Department of Economics and Management of the University of Trento (seminar room, 1st floor).

The seminar will be held in English.