Testing Lorenz Curves with Non-Simple Random Samples
指出，现有检验洛伦兹曲线优劣的统计方法大多假设简单随机抽样，但实际数据常来自分层、整群或多阶段抽样。作者利用Bahadur表示推导了这些复杂抽样下洛伦兹曲线和广义洛伦兹曲线各点的协方差结构，并说明忽略抽样方法会导致推断错误。
Simple random sampling has been assumed in most statistical inference procedures developed to test Lorenz dominance and other partial ordering conditions. This note, using the Bahadur representation, derives the (asymptotic) covariance structures of the Lorenz and generalized Lorenz ordinates for stratified, cluster and multistage samples. The comparison of these covariance structures illustrates the necessity of taking the sampling method into account in inference testing.