Income inequality estimators are biased in small samples, leading generally to an underestimation. This aspect deserves particular attention when estimating inequality in small domains and performing small area estimation at the area level. We propose a bias correction framework for a large class of inequality measures comprising the Gini Index, the Generalized Entropy and the Atkinson index families by accounting for complex survey designs. The proposed methodology does not require any parametric assumption on income distribution, being very flexible. Design-based performance evaluation of our proposal has been carried out using EU-SILC data, their results show a noticeable bias reduction for all the measures. Lastly, an illustrative example of application in small area estimation confirms that ignoring ex-ante bias correction determines model misspecification.

翻译：收入不平等估计量在小样本中存在偏差，通常导致低估。这一问题在估计小域不平等以及进行区域级小面积估计时尤为值得关注。我们针对一大类不平等度量指标（包括基尼指数、广义熵和Atkinson指数族）提出了一种偏差校正框架，并考虑了复杂调查设计。所提出的方法无需对收入分布作任何参数假设，具有高度灵活性。我们利用EU-SILC数据对所提方法进行了基于设计的性能评估，结果显示所有度量指标的偏差均显著降低。最后，在小面积估计中的应用示例表明，忽视事前偏差校正会导致模型误设。