Likelihood Ratio Tests for Lorenz Dominance
提出基于似然比的拟合优度检验，用于检验洛伦兹占优、交叉洛伦兹曲线和三阶随机占优假设，并通过模拟和COVID-19区域死亡数据验证方法。
In testing hypotheses pertaining to Lorenz dominance (LD), researchers have examined second- and third-order stochastic dominance using empirical Lorenz processes and integrated stochastic processes with the aid of bootstrap analysis. Among these topics, analysis of third-order stochastic dominance (TSD) based on the notion of risk aversion has been examined using crossing (generalized) Lorenz curves. These facts motivated the present study to characterize distribution pairs displaying the TSD without second-order (generalized Lorenz) dominance. It further motivated the development of likelihood ratio (LR) goodness-of-fit tests for examining the respective hypotheses of the LD, crossing (generalized) Lorenz curves, and TSD through approximate Chi-squared distributions. The proposed LR tests were assessed using simulated distributions, and applied to examine the COVID-19 regional death counts of bivariate samples collected by the World Health Organization between March 2020 and February 2021.