ABSTRACT The Gini index has been widely used as a measure of income (or wealth) inequality in social sciences. To construct a confidence interval for the difference of two Gini indices from the paired samples, Wang and Zhao [‘Jackknife Empirical Likelihood for Comparing Two Gini Indices’, The Canadian Journal of Statistics, 44(1), 102–119] used a profile jackknife empirical likelihood. However, the computing cost with the profile empirical likelihood could be very expensive. In this paper, we propose an alternative approach of the jackknife empirical likelihood method to reduce the computational cost. We also investigate the adjusted jackknife empirical likelihood and the bootstrap-calibrated jackknife empirical likelihood to improve coverage accuracy for small samples. Simulations show that the proposed methods perform better than Wang and Zhao's methods in terms of coverage accuracy and computational time. Real data applications demonstrate that the proposed methods work very well in practice.

中文翻译：

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减少用于比较两个相关基尼指数的 jackknife 经验似然计算

摘要 基尼指数在社会科学中被广泛用作衡量收入（或财富）不平等的指标。为了构建配对样本中两个基尼系数差异的置信区间，Wang 和 Zhao ['Jackknife Empirical Likelihood for Comparing Two Gini Indices', The Canadian Journal of Statistics, 44(1), 102–119] 使用了一个配置文件jackknife 经验可能性。然而，具有轮廓经验可能性的计算成本可能非常昂贵。在本文中，我们提出了一种替代的折刀经验似然法来降低计算成本。我们还研究了调整后的 jackknife 经验似然和 bootstrap 校准的 jackknife 经验似然，以提高小样本的覆盖精度。仿真表明，所提出的方法在覆盖精度和计算时间方面优于王和赵的方法。实际数据应用表明，所提出的方法在实践中非常有效。