In this paper, the problem of testing the hypothesis of linear combination of k-sample means of high-dimensional data is investigated under a low-dimensional factor model. We propose a new test and derive that the asymptotic distribution of the test statistic is a weighted distribution of independent chi-squared distribution of 1 degree of freedom under the null hypothesis and mild conditions. We provide numerical studies on both sizes and powers to illustrate performance of the proposed test.

中文翻译：

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低维因子模型下均值线性假设的高维检验

本文研究了在低维因子模型下检验高维数据的k个样本均值线性组合假设的问题。我们提出了一个新的检验，并推导出检验统计量的渐近分布是在零假设和温和条件下的 1 个自由度的独立卡方分布的加权分布。我们提供了关于大小和功率的数值研究，以说明所提议测试的性能。