Statistical Analysis of the Hirsch Index

The Hirsch index (commonly referred to as h -index) is a biblio- metric indicator which is widely recognized as effective for measuring the scientific production of a scholar since it summarizes si ze and impact of the research output. In a formal setting, the h -index is actually an empirical functional of the distribution of the citation counts received by the scholar. Under this approach, the asymptotic theory for the empirica l h - index has been recently exploited when the citation counts f ollow a continuous distribution and, in particular, variance esti mation has been considered for the Pareto-type and the Weibull-type di stribu- tion families. However, in bibliometric applications, cit ation counts display a distribution supported by the integers. Thus, we p rovide general properties for the empirical h -index under the small- and large-sample settings. In addition, we also introduce consistent nonparametric va riance estimation, which allows for the implemention of large-sam ple set estimation for the theoretical h -index