Asymptotics for the Hirsch Index
CentER Discussion Paper Series No. 2007-86
12 Pages Posted: 4 Nov 2007
Date Written: October 25, 2007
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 the Web 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.
Keywords: asymptotic normality; confidence interval; extreme value theory; research output; scientometrics; tail empirical process.
JEL Classification: C13, C14
Suggested Citation: Suggested Citation