Permutation Tests for Comparing Inequality Measures
针对重尾分布下有限样本中不平等指标检验表现不佳的问题，提出了蒙特卡洛置换和自助法，覆盖广义熵、Atkinson和基尼指数，模拟显示该方法能有效控制检验规模并提高功效。
Asymptotic and bootstrap tests for inequality measures are known to perform poorly in finite samples when the underlying distribution is heavy-tailed. We propose Monte Carlo permutation and bootstrap methods for the problem of testing the equality of inequality measures between two samples. Results cover the Generalized Entropy class, which includes Theil’s index, the Atkinson class of indices, and the Gini index. We analyze finite-sample and asymptotic conditions for the validity of the proposed methods, and we introduce a convenient rescaling to improve finite-sample performance. Simulation results show that size correct inference can be obtained with our proposed methods despite heavy tails if the underlying distributions are sufficiently close in the upper tails. Substantial reduction in size distortion is achieved more generally. Studentized rescaled Monte Carlo permutation tests outperform the competing methods we consider in terms of power.