In this paper, a new test procedure is proposed to test a linear hypothesis of k-sample mean vectors in highdimensional normal models with heteroskedasticity. The motivation is on the basis of the generalized likelihood ratio method and the Bennett transformation. The asymptotic distributions of the new test are derived under null and local alternative hypotheses under mild conditions. Simulation results show that the new test can control the nominal level reasonably and has greater power than competing tests in some cases. Moreover, numerical studies illustrate that our proposed test can also be applied to non-normal data.

中文翻译：

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高维数据中$k$-sample均值的线性假设检验

在本文中，提出了一种新的测试程序来测试具有异方差性的高维正态模型中 k 样本均值向量的线性假设。动机是基于广义似然比方法和 Bennett 变换。新检验的渐近分布是在温和条件下的零假设和局部替代假设下得出的。仿真结果表明，新测试能够合理控制标称电平，并且在某些情况下比竞争测试具有更大的威力。此外，数值研究表明，我们提出的测试也可以应用于非正态数据。