Test for mean matrix in GMANOVA model under heteroscedasticity and non-normality for high-dimensional data

IF 0.4 Q4 STATISTICS & PROBABILITY Theory of Probability and Mathematical Statistics Pub Date : 2023-10-03 DOI:10.1090/tpms/1200
Takayuki Yamada, Tetsuto Himeno, Annika Tillander, Tatjana Pavlenko
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Abstract

This paper is concerned with the testing bilateral linear hypothesis on the mean matrix in the context of the generalized multivariate analysis of variance (GMANOVA) model when the dimensions of the observed vector may exceed the sample size, the design may become unbalanced, the population may not be normal, or the true covariance matrices may be unequal. The suggested testing methodology can treat many problems such as the one- and two-way MANOVA tests, the test for parallelism in profile analysis, etc., as specific ones. We propose a bias-corrected estimator of the Frobenius norm for the mean matrix, which is a key component of the test statistic. The null and non-null distributions are derived under a general high-dimensional asymptotic framework that allows the dimensionality to arbitrarily exceed the sample size of a group, thereby establishing consistency for the testing criterion. The accuracy of the proposed test in a finite sample is investigated through simulations conducted for several high-dimensional scenarios and various underlying population distributions in combination with different within-group covariance structures. Finally, the proposed test is applied to a high-dimensional two-way MANOVA problem for DNA microarray data.
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高维数据异方差和非正态下GMANOVA模型均值矩阵的检验
本文讨论了在广义多元方差分析(GMANOVA)模型中,当观测向量的维度可能超过样本量、设计可能变得不平衡、总体可能不正常或真协方差矩阵不相等时,在平均矩阵上检验双边线性假设的问题。所建议的测试方法可以将许多问题,如单、双向方差分析测试、配置文件分析中的并行性测试等,作为具体的问题来处理。我们提出了Frobenius范数的偏校正估计的平均矩阵,这是检验统计量的一个关键组成部分。零分布和非零分布是在一般的高维渐近框架下推导出来的,该框架允许维数任意超过一个组的样本量,从而建立了检验标准的一致性。通过对几个高维场景和各种潜在种群分布结合不同组内协方差结构的模拟,研究了在有限样本中提出的测试的准确性。最后,将提出的测试应用于DNA微阵列数据的高维双向方差分析问题。
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CiteScore
1.30
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发文量
22
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