The study of income inequality is important for predicting the wealth of a country. There is an increasing number of publications where the authors call for the use of several indices simultaneously to better account for the wealth distribution. Due to the fact that income data are usually collected through sample surveys, the sampling properties of income inequality measures should not be overlooked. The most widely used inequality measure is the Gini index, and its inferential aspects have been deeply investigated. An alternative inequality index could be the Bonferroni inequality index, although less attention on its inference has been paid in the literature. The aim of this paper is to address the inference of the Bonferroni index in a finite population framework. The Bonferroni index is linearized by differentiation with respect to the sample indicators which allows for conducting a valid inference. Furthermore, the linearized variables are used to evaluate the effects of the different observations on the Bonferroni and Gini indices. The result demonstrates once for all that the former is more sensitive to the lowest incomes in the distribution than the latter.

中文翻译：

---

Bonferroni 不等式指数的线性化和方差估计

收入不平等的研究对于预测一个国家的财富很重要。越来越多的出版物要求作者同时使用多个指数来更好地解释财富分配。由于收入数据通常是通过抽样调查收集的，因此不应忽视收入不平等测度的抽样性质。使用最广泛的不平等衡量标准是基尼指数，其推论方面已得到深入研究。另一种不平等指数可以是 Bonferroni 不平等指数，尽管文献中对其推论的关注较少。本文的目的是在有限人口框架中解决 Bonferroni 指数的推论问题。Bonferroni 指数通过对样本指标的微分进行线性化，这允许进行有效的推理。此外，线性化变量用于评估不同观察结果对 Bonferroni 和 Gini 指数的影响。结果一劳永逸地表明，前者对分配中最低收入的敏感度高于后者。