Semi-parametric regression estimation of the tail index

Mofei Jia, Emanuele Taufer, Maria Michela Dickson

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


Consider a distribution F with regularly varying tails of index −α. An estimation strategy for α, exploiting the relation between the behavior of the tail at infinity and of the characteristic function at the origin, is proposed. A semi-parametric regression model does the job: a nonparametric 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. Theoretical properties of the proposed method are derived and simulations show the 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.

Original languageEnglish
Pages (from-to)224-248
Number of pages25
JournalElectronic Journal of Statistics
Issue number1
Publication statusPublished - 2018


  • Empirical characteristic function
  • Heavy-tailed distributions
  • Regular variation
  • Tail index
  • Zipf’s law


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