Asymptotics for the Hirsch index

J. Beirlant, J.H.J. Einmahl

Research output: Contribution to journalArticleScientificpeer-review

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:√h/(1+nf(h)), 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.
Original languageEnglish
Pages (from-to)355-364
JournalScandinavian Journal of Statistics
Volume37
Publication statusPublished - 2010

Fingerprint

Hirsch Index
Citations
Pareto
Bibliometrics
Extreme Value Theory
Pairwise Comparisons
Weibull
Asymptotic Theory
Asymptotic Normality
Confidence interval
Sample Size
Rate of Convergence
Simulation Study
Output

Cite this

@article{ba21d4c8f0864f52bb5a90f54a4b8b11,
title = "Asymptotics for the Hirsch index",
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:√h/(1+nf(h)), 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.",
author = "J. Beirlant and J.H.J. Einmahl",
note = "Appeared earlier as CentER DP 2007-86",
year = "2010",
language = "English",
volume = "37",
pages = "355--364",
journal = "Scandinavian Journal of Statistics",
issn = "0303-6898",

}

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

In: Scandinavian Journal of Statistics, Vol. 37, 2010, p. 355-364.

Research output: Contribution to journalArticleScientificpeer-review

TY - JOUR

T1 - Asymptotics for the Hirsch index

AU - Beirlant, J.

AU - Einmahl, J.H.J.

N1 - Appeared earlier as CentER DP 2007-86

PY - 2010

Y1 - 2010

N2 - 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:√h/(1+nf(h)), 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.

AB - 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:√h/(1+nf(h)), 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.

M3 - Article

VL - 37

SP - 355

EP - 364

JO - Scandinavian Journal of Statistics

JF - Scandinavian Journal of Statistics

SN - 0303-6898

ER -