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2018 Semi-parametric regression estimation of the tail index
Mofei Jia, Emanuele Taufer, Maria Michela Dickson
Electron. J. Statist. 12(1): 224-248 (2018). DOI: 10.1214/18-EJS1394


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 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.


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Mofei Jia. Emanuele Taufer. Maria Michela Dickson. "Semi-parametric regression estimation of the tail index." Electron. J. Statist. 12 (1) 224 - 248, 2018.


Received: 1 May 2017; Published: 2018
First available in Project Euclid: 12 February 2018

zbMATH: 1387.62068
MathSciNet: MR3763071
Digital Object Identifier: 10.1214/18-EJS1394

Primary: 62G32
Secondary: 62J05


Vol.12 • No. 1 • 2018
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