赫希指数的统计分析
Statistical analysis of the Hirsch Index
摘要：
赫希指数（英语：Hirsch index）是一种文献计量学指标，被广泛认为是衡量学者科学成果的有效指标，因为它总结了研究成果的规模和影响。在正式的设置中，h指数实际上是学者收到的引用计数分布的经验泛函。根据这种方法，渐近理论的经验h-指数已被利用时，引用计数遵循连续分布，特别是方差估计已被认为是帕累托型和威布尔型分布的家庭。然而，在文献计量学应用中，引用计数显示由整数支持的分布。因此，我们提供了小样本和大样本设置下的经验h指数的一般性质。此外，我们还引入了相容的非参数方差估计，它允许实现理论h-指标的大样本集估计。
英文摘要：
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.
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