Economic inequalities referring to specific regions are crucial in deepening spatial heterogeneity. Income surveys are generally planned to produce reliable estimates at countries or macroregion levels, thus we implement a small area model for a set of inequality measures (Gini, Relative Theil and Atkinson indexes) to obtain microregion estimates. Considering that inequality estimators are unit-interval defined with skewed and heavy-tailed distributions, we propose a Bayesian hierarchical model at area level involving a Beta mixture. An application on EU-SILC data is carried out and a design-based simulation is performed. Our model outperforms in terms of bias, coverage and error the standard Beta regression model. Moreover, we extend the analysis of inequality estimators by deriving their approximate variance functions.

翻译：涉及特定区域的经济不平等是加深空间差异的关键所在,一般计划进行收入调查,以便在国家或宏观区域各级得出可靠的估计数,因此,我们实施一套不平等措施(吉尼、相对Theil和阿特金森指数)的小型区域模型,以获得微观区域估计数;考虑到不平等估计数字是单位间隔,以斜面和重尾分分布来界定,我们提议在贝塔混合物地区一级采用巴耶斯等级模型;对欧盟-SILC数据进行应用,并进行基于设计的模拟;我们的模型在偏见、覆盖面和误差方面优于贝塔标准回归模型;此外,我们扩大对不平等估计值的分析,得出其大致差异功能。