不等式约束条件下经验似然法在两总体中位数检验中的应用

Empirical likelihood method employed in the comparison of two sample medians under inequality constraints

本文中,Owen引入的经验似然方法被用于参数空间带不等式约束的两总体中位数的比较.迄今为止,还没有人研究过该问题.这是因为,在构造经验似然函数过程中所使用的辅助函数不是光滑函数,因而不是凸函数,从而使研究难度大大增加.然而,通过引入经验过程的办法,本文很巧妙地解决了此问题.根据经验过程,本文证明了两中位数比较的经验似然比检验统计量的极限分布要么是单一的卡方分布,要么是两个卡方分布的等权混合分布.这一理论结果得到了模拟运算结果的有力支持.

In this article, the empirical likelihood introduced by Owen is applied to test the medians from two populations with inequality constraints imposed on the parameter space. So far, no research work in this area has ever touched the issue since the auxiliary function in the construction of empirical likelihood function is not smooth and thus is not convex. This makes the research work much more complicated. However, we solve the problem by introduce in empirical processes. Theoretically, we proved that the limiting distribution of the empirical likelihood ratio test statistic is either a single chi-square distribution or the equally weighted mixture of two chi-square distributions. What is more, this theory is convincingly supported by commendable simulation results.