高维数据下异方差与非正态性时GMANOVA模型中均值矩阵的检验
Test for mean matrix in GMANOVA model under heteroscedasticity and non-normality for high-dimensional data
AI总结：
本文针对高维GMANOVA模型在异方差和非正态条件下提出基于Frobenius范数偏差校正估计量的均值矩阵检验方法，推导其渐近分布并验证一致性，通过模拟和DNA微阵列数据应用证明其有效性。
摘要：
本文研究在广义多元方差分析（GMANOVA）模型背景下，当观测向量的维数可能超过样本量、设计可能不平衡、总体可能非正态或真实协方差矩阵可能不相等时，对均值矩阵的双边线性假设进行检验的问题。所提出的检验方法可以将许多问题作为特例来处理，例如单向和双向MANOVA检验、轮廓分析中的平行性检验等。我们提出了均值矩阵Frobenius范数的一个偏差校正估计量，它是检验统计量的关键组成部分。在一般的高维渐近框架下推导了原假设分布和备择假设分布，该框架允许维数任意超过某一组的样本量，从而建立了检验准则的一致性。通过在若干高维情景以及各种潜在总体分布与不同组内协方差结构相结合的情况下进行的模拟，研究了所提检验在有限样本下的准确性。最后，将所提检验应用于DNA微阵列数据的一个高维双向MANOVA问题。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
