Abstract In this paper, the problem of simultaneously testing mean vector and covariance matrix of one-sample population is investigated in high-dimensional settings. We propose a new test statistic and obtain its asymptotic distributions under null and local alternative hypotheses, respectively. Our asymptotic result for proposed test does not need some conditions such as linearity between the sample size and dimension used in existing studies. Simulation results also demonstrate our new test not only can control reasonably the nominal level but also has greater empirical powers than competing tests.

中文翻译：

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高维设置中均值向量和协方差矩阵的同时测试

摘要 本文研究了在高维环境下同时检验单样本总体的均值向量和协方差矩阵的问题。我们提出了一个新的检验统计量，并分别在原假设和局部替代假设下获得了它的渐近分布。我们提议检验的渐近结果不需要某些条件，例如现有研究中使用的样本大小和维度之间的线性关系。仿真结果还表明，我们的新测试不仅可以合理控制标称水平，而且比竞争测试具有更大的经验效力。