Statistical Analysis of the Hirsch Index

Abstract. The Hirsch index (commonly referred to as h‐index) is a bibliometric indicator which is widely recognized as effective for measuring the scientific production of a scholar since it summarizes size 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 empirical h‐index has been recently exploited when the citation counts follow a continuous distribution and, in particular, variance estimation has been considered for the Pareto‐type and the Weibull‐type distribution families. However, in bibliometric applications, citation counts display a distribution supported by the integers. Thus, we provide general properties for the empirical h‐index under the small‐ and large‐sample settings. In addition, we also introduce consistent non‐parametric variance estimation, which allows for the implementation of large‐sample set estimation for the theoretical h‐index.