Asymptotics for the Hirsch Index

J. Beirlant, J.H.J. Einmahl

Research output: Working paperDiscussion paperOther research output

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Abstract

The last decade methods for quantifying the research output of individual researchers have become quite popular in academic policy making. The h- index (Hirsch, 2005) constitutes an interesting quality measure that has attracted a lot of attention recently. It is now a standard measure available for instance on theWeb of Science. In this paper we establish the asymptotic normality of the empirical h-index. The rate of convergence is non-standard: ph=(1 + nf(h)), where f is the density of the citation distribution and n the number of publications of a researcher. In case that the citations follow a Pareto-type or a Weibull-type distribution as defined in extreme value theory, our general result nicely specializes to results that are useful for constructing confidence intervals for the h-index.
Original languageEnglish
Place of PublicationTilburg
PublisherEconometrics
Number of pages12
Volume2007-86
Publication statusPublished - 2007

Publication series

NameCentER Discussion Paper
Volume2007-86

Fingerprint

Hirsch Index
Citations
Extreme Value Theory
Quality Measures
Weibull
Pareto
Asymptotic Normality
Confidence interval
Rate of Convergence
Output

Keywords

  • Asymptotic normality
  • confidence interval
  • extreme value theory
  • research output
  • scientometrics
  • tail empirical process.

Cite this

Beirlant, J., & Einmahl, J. H. J. (2007). Asymptotics for the Hirsch Index. (CentER Discussion Paper; Vol. 2007-86). Tilburg: Econometrics.
Beirlant, J. ; Einmahl, J.H.J. / Asymptotics for the Hirsch Index. Tilburg : Econometrics, 2007. (CentER Discussion Paper).
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Beirlant, J & Einmahl, JHJ 2007 'Asymptotics for the Hirsch Index' CentER Discussion Paper, vol. 2007-86, Econometrics, Tilburg.

Asymptotics for the Hirsch Index. / Beirlant, J.; Einmahl, J.H.J.

Tilburg : Econometrics, 2007. (CentER Discussion Paper; Vol. 2007-86).

Research output: Working paperDiscussion paperOther research output

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N2 - The last decade methods for quantifying the research output of individual researchers have become quite popular in academic policy making. The h- index (Hirsch, 2005) constitutes an interesting quality measure that has attracted a lot of attention recently. It is now a standard measure available for instance on theWeb of Science. In this paper we establish the asymptotic normality of the empirical h-index. The rate of convergence is non-standard: ph=(1 + nf(h)), where f is the density of the citation distribution and n the number of publications of a researcher. In case that the citations follow a Pareto-type or a Weibull-type distribution as defined in extreme value theory, our general result nicely specializes to results that are useful for constructing confidence intervals for the h-index.

AB - The last decade methods for quantifying the research output of individual researchers have become quite popular in academic policy making. The h- index (Hirsch, 2005) constitutes an interesting quality measure that has attracted a lot of attention recently. It is now a standard measure available for instance on theWeb of Science. In this paper we establish the asymptotic normality of the empirical h-index. The rate of convergence is non-standard: ph=(1 + nf(h)), where f is the density of the citation distribution and n the number of publications of a researcher. In case that the citations follow a Pareto-type or a Weibull-type distribution as defined in extreme value theory, our general result nicely specializes to results that are useful for constructing confidence intervals for the h-index.

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Beirlant J, Einmahl JHJ. Asymptotics for the Hirsch Index. Tilburg: Econometrics. 2007. (CentER Discussion Paper).