This paper is concerned with the problem of comparing the population means of two groups of independent observations. An approximate randomization test procedure based on the test statistic of Chen & Qin (2010) is proposed. The asymptotic behavior of the test statistic as well as the randomized statistic is studied under weak conditions. In our theoretical framework, observations are not assumed to be identically distributed even within groups. No condition on the eigenstructure of the covariance matrices is imposed. And the sample sizes of two groups are allowed to be unbalanced. Under general conditions, all possible asymptotic distributions of the test statistic are obtained. We derive the asymptotic level and local power of the approximate randomization 20 test procedure. Our theoretical results show that the proposed test procedure can adapt to all possible asymptotic distributions of the test statistic and always has correct test level asymptotically. Also, the proposed test procedure has good power behavior. Our numerical experiments show that the proposed test procedure has favorable performance compared with several alternative test procedures.
翻译:本文涉及比较两组独立观测的人口手段的问题。 根据Chen & Qin(2010年)的测试统计,提出了一种近似随机化测试程序。对测试统计的无症状行为以及随机化统计在薄弱的条件下进行了研究。在我们的理论框架内,不假定观测在组内分布相同。对共变矩阵的均匀结构没有附加任何条件。允许两个组的样本大小不平衡。在一般条件下,获得测试统计的所有可能的无症状分布。我们得出了近似随机化20个测试程序的无症状水平和地方力量。我们的理论结果表明,拟议的测试程序可以适应所有可能的测试统计的无症状分布,并且始终具有正确的测试水平。此外,拟议的测试程序具有良好的能量行为。我们的数字实验表明,与几种替代测试程序相比,拟议的测试程序具有有利的性。