Beirlant, J; Einmahl, JHJ. 2010. Asymptotics for the Hirsch Index. SCANDINAVIAN JOURNAL OF STATISTICS 37 (3): 355-364

[Eugene Garfield]

Beirlant, J; Einmahl, JHJ. 2010. Asymptotics for the Hirsch Index. 
SCANDINAVIAN JOURNAL OF STATISTICS 37 (3): 355-364..

Author Full Name(s): Beirlant, Jan; Einmahl, John H. J.
Language: English
Document Type: Article

Author Keywords: asymptotic normality; citation counts; extreme value theory; 
Hirsch index; research output; tail empirical process
KeyWords Plus: WEIBULL TAIL-COEFFICIENT

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: root 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.

Addresses: [Einmahl, John H. J.] Tilburg Univ, Dept Econometr & Operat Res & 
Ctr, NL-5000 LE Tilburg, Netherlands; [Beirlant, Jan] Katholieke Univ Leuven, 
Louvain, Belgium

Reprint Address: Einmahl, JHJ, Tilburg Univ, Dept Econometr & Operat Res & 
Ctr, POB 90153, NL-5000 LE Tilburg, Netherlands.

E-mail Address: j.h.j.einmahl at uvt.nl
ISSN: 0303-6898
DOI: 10.1111/j.1467-9469.2010.00694.x
fulltext: http://onlinelibrary.wiley.com/doi/10.1111/j.1467-
9469.2010.00694.x/abstract