Statistical analysis of the Hirsch Index

TL;DR

This paper provides a comprehensive statistical analysis of the h-index, addressing its properties for integer-valued citation counts and introducing nonparametric variance estimation methods for more accurate bibliometric evaluations.

Contribution

It extends the asymptotic theory of the h-index to integer-valued citation distributions and proposes a consistent nonparametric variance estimator.

Findings

General properties of the empirical h-index for small and large samples.

Introduction of a consistent nonparametric variance estimator.

Enhanced methods for large-sample set estimation of the theoretical h-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 nonparametric variance estimation, which allows for the implemention of large-sample set estimation for the theoretical h-index.