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Asymptotics for the Hirsch Index

Author

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  • JAN BEIRLANT
  • JOHN H. J. EINMAHL

Abstract

. The last decade methods for quantifying the research output of individual researchers have become quite popular in academic policy making. The h‐index (or Hirsch index) constitutes an interesting combined bibliometric volume/impact indicator that has attracted a lot of attention recently. It is now a common indicator, available for instance on the Web of Science. In this article, we establish the asymptotic normality of the empirical h‐index. The rate of convergence is non‐standard: , where f is the density of the citation distribution and n is the number of publications of a researcher. In case that the citations follow a Pareto‐type respectively a Weibull‐type distribution as defined in extreme value theory, our general result specializes well to results that are useful for practical purposes such as the construction of confidence intervals and pairwise comparisons for the h‐index. A simulation study for the Pareto‐type case shows that the asymptotic theory works well for moderate sample sizes already.

Suggested Citation

  • Jan Beirlant & John H. J. Einmahl, 2010. "Asymptotics for the Hirsch Index," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(3), pages 355-364, September.
    • Handle: RePEc:bla:scjsta:v:37:y:2010:i:3:p:355-364
    DOI: 10.1111/j.1467-9469.2010.00694.x
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    References listed on IDEAS

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    1. Einmahl, John H. J., 1997. "Poisson and Gaussian approximation of weighted local empirical processes," Stochastic Processes and their Applications, Elsevier, vol. 70(1), pages 31-58, October.
    2. Jean Diebolt & Laurent Gardes & Stéphane Girard & Armelle Guillou, 2008. "Bias-reduced estimators of the Weibull tail-coefficient," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 17(2), pages 311-331, August.
    3. Leo Egghe & Ronald Rousseau, 2006. "An informetric model for the Hirsch-index," Scientometrics, Springer;Akadémiai Kiadó, vol. 69(1), pages 121-129, October.
    4. Wolfgang Glänzel, 2006. "On the h-index - A mathematical approach to a new measure of publication activity and citation impact," Scientometrics, Springer;Akadémiai Kiadó, vol. 67(2), pages 315-321, May.
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    Citations

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    Cited by:

    1. Krisztina Barcza & András Telcs, 2009. "Paretian publication patterns imply Paretian Hirsch index," Scientometrics, Springer;Akadémiai Kiadó, vol. 81(2), pages 513-519, November.
    2. Paola Cerchiello & Paolo Giudici, 2014. "How to measure the quality of financial tweets," DEM Working Papers Series 069, University of Pavia, Department of Economics and Management.
    3. J. Martin Zyl, 2013. "The generalized Pareto distribution fitted to research outputs of countries," Scientometrics, Springer;Akadémiai Kiadó, vol. 94(3), pages 1099-1109, March.
    4. Baccini, A. & Barabesi, L. & Marcheselli, M. & Pratelli, L., 2012. "Statistical inference on the h-index with an application to top-scientist performance," Journal of Informetrics, Elsevier, vol. 6(4), pages 721-728.
    5. Wolfgang Glänzel, 2010. "The role of the h-index and the characteristic scores and scales in testing the tail properties of scientometric distributions," Scientometrics, Springer;Akadémiai Kiadó, vol. 83(3), pages 697-709, June.
    6. Paola Cerchiello & Paolo Giudici, 2013. "H Index: A Statistical Proposal," DEM Working Papers Series 039, University of Pavia, Department of Economics and Management.
    7. Paola Cerchiello & Paolo Giudici, 2014. "On a statistical h index," Scientometrics, Springer;Akadémiai Kiadó, vol. 99(2), pages 299-312, May.
    8. Paola Cerchiello & Paolo Giudici, 2014. "Financial big data analysis for the estimation of systemic risks," DEM Working Papers Series 086, University of Pavia, Department of Economics and Management.
    9. Wolfgang Glänzel & Henk F. Moed, 2013. "Opinion paper: thoughts and facts on bibliometric indicators," Scientometrics, Springer;Akadémiai Kiadó, vol. 96(1), pages 381-394, July.
    10. John Panaretos & Chrisovaladis Malesios, 2009. "Assessing scientific research performance and impact with single indices," Scientometrics, Springer;Akadémiai Kiadó, vol. 81(3), pages 635-670, December.
    11. Paola Cerchiello & Paolo Giudici, 2015. "A Bayesian h-index: how to measure research impact," DEM Working Papers Series 102, University of Pavia, Department of Economics and Management.
    12. Xu, Qifa & Chen, Lu & Jiang, Cuixia & Yu, Keming, 2020. "Mixed data sampling expectile regression with applications to measuring financial risk," Economic Modelling, Elsevier, vol. 91(C), pages 469-486.

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    More about this item

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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