We consider the estimation of the relative median poverty gap (RMPG) at the level of Italian provinces by using data from the European Union Survey on Income and Living Conditions. The overall sample size does not allow reliable estimation of income‐distribution‐related parameters at the provincial level; therefore, small area estimation techniques must be used. The specific challenge in estimating the RMPG is that, as it summarizes the income distribution of the poor, samples for estimating it for small subpopulations are even smaller than those available in other parameters. We propose a Bayesian strategy where various parameters summarizing the distribution of income at the provincial level are modelled by means of a multivariate small area model. To estimate the RMPG, we relate these parameters to a distribution describing income, namely the generalized beta distribution of the second kind. Posterior draws from the multivariate model are then used to generate draws for the distribution's area‐specific parameters and then of the RMPG defined as their functional.

中文翻译：

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小范围估算相对中位数贫困差距的功能方法

我们使用来自欧盟收入和生活状况调查的数据，考虑对意大利各省相对贫困线的中位数（RMPG）进行估算。总体样本量无法可靠地估算省级与收入分配相关的参数；因此，必须使用小面积估计技术。估算RMPG的具体挑战在于，由于它总结了穷人的收入分布，因此用于估计小亚人群的样本的规模甚至比其他参数中可用的样本还要小。我们提出了一种贝叶斯策略，其中通过多元小面积模型对总结省级收入分配的各种参数进行建模。为了估算RMPG，我们将这些参数与描述收入的分布相关联，即第二种广义的beta分布。然后使用多元模型的后验绘图生成分布区域特定参数的绘图，然后将RMPG定义为函数的绘图。