A Behrens-Fisher problem for general factor models in high dimensions
A Behrens-Fisher problem for general factor models in high dimensions
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DOI：
10.1016/j.jmva.2023.105162
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发表时间：
2023-05
期刊：
影响因子：
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通讯作者：
Masashi Hyodo;T. Nishiyama;T. Pavlenko
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文献类型：
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作者：
Masashi Hyodo;T. Nishiyama;T. Pavlenko
我们重新审视了著名的Beynolds-Fisher问题，在一个原始的和具有挑战性的高维框架，并提出了一个测试程序，它可以容纳一个低维的潜在因素模型。所开发的推理框架是一般的，因为它适用于潜在的人口可能是非正态的问题，人口平均向量的维度可能远远超过样本量，设计可能是不平衡的，负载因子维度可能是不同的。在高维渐近制度下，结合相当弱的技术条件，我们表明，零极限分布的检验统计量遵循加权混合卡方分布，这只取决于噪声协方差矩阵的频谱和潜在的因素的数量。由于后者通常是未知的，在实践中，我们利用的估计过程，建立在随机矩阵理论的最新进展。建立了该检验的渐近功效。数值研究证实了良好的分析性能的新的测试相比，有利的现有程序在类似的情况下使用。真实的数据的应用证明与白血病数据集的研究。
We revisit the well-known Behrens–Fisher problem in an original and challenging high-dimensional framework, and propose a testing procedure which accommodates a low-dimensional latent factor model. The developed inferential framework is general, as it applies to problems where the underlying populations may be non-normal, the dimension of the population mean vectors may highly exceed the sample size, the design may be unbalanced, and the loading factor dimensions may be different. Under a high-dimensional asymptotic regime, combined with fairly weak technical conditions, we show that null limiting distributions of the test statistics follow a weighted mixture of chi-square distributions, which depends only on the spectrum of the noise covariance matrix and the number of latent factors. As these latter are usually unknown in practice, we exploit an estimation procedure which builds on recent advances in random matrix theory. The asymptotic power of the proposed test is established. A numerical study confirms good analytical properties of the new test that compares favorably to existing procedures used in a similar context. Real data applications are demonstrated with a study of a leukemia data set.