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.

Semi-parametric regression estimation of the tail index / Jia, Mofei; Taufer, Emanuele; Dickson, Maria Michela. - In: ELECTRONIC JOURNAL OF STATISTICS. - ISSN 1935-7524. - ELETTRONICO. - 2018, 12:1(2018), pp. 224-248. [10.1214/18-EJS1394]

Semi-parametric regression estimation of the tail index

Jia, Mofei;Taufer, Emanuele;Dickson, Maria Michela
2018-01-01

Abstract

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.
2018
1
Jia, Mofei; Taufer, Emanuele; Dickson, Maria Michela
Semi-parametric regression estimation of the tail index / Jia, Mofei; Taufer, Emanuele; Dickson, Maria Michela. - In: ELECTRONIC JOURNAL OF STATISTICS. - ISSN 1935-7524. - ELETTRONICO. - 2018, 12:1(2018), pp. 224-248. [10.1214/18-EJS1394]
File in questo prodotto:
File Dimensione Formato  
2018 - EJS - Semi-parametric regression of the tail index.pdf

accesso aperto

Descrizione: Articolo in versione pubblicata
Tipologia: Versione editoriale (Publisher’s layout)
Licenza: Creative commons
Dimensione 341.51 kB
Formato Adobe PDF
341.51 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/200362
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 5
  • ???jsp.display-item.citation.isi??? 5
social impact