Linearization and Variance Estimation of the Bonferroni Inequality Index
研究了Bonferroni不平等指数在有限总体中的推断问题，通过线性化方法实现有效推断，并发现该指数比Gini指数对低收入更敏感。
Abstract 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.