Testing homogeneity of mean vectors under heteroscedasticity in high-dimension
Testing homogeneity of mean vectors under heteroscedasticity in high-dimension
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DOI：
10.1016/j.jmva.2015.02.005
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发表时间：
2015-07
期刊：
影响因子：
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通讯作者：
Takayuki Yamada;Tetsuto Himeno
中科院分区：
文献类型：
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作者：
Takayuki Yamada;Tetsuto Himeno
本文关注的是均值向量同质性的检验问题。测试问题不假设公共协方差矩阵。由于假设和协方差矩阵的无偏估计，我们提出了基于变异矩阵的检验统计量。当每个样本大小和维数在一般总体分布下趋于无穷大时，导出限制零分布和非零分布，其中包括具有有限四阶矩的椭圆分布或 Chen 和 Qing (2010) 中假设的分布。在两个样本的情况下，我们提出的检验具有与 Chen 和 Qin（2010）的检验相同的渐近功效。此外，我们发现我们提出的检验与 Fujikoshi 等人提出的 Dempster 多元方差分析迹统计量具有相同的渐近功效。 （2004）对于所有群体的总体分布都是具有共同协方差矩阵的多元正态分布的情况。进行了小规模模拟研究，以将第一类实际误差概率与标称误差概率进行比较。
This paper is concerned with the problem of testing the homogeneity of mean vectors. The testing problem is without assuming common covariance matrix. We proposed a testing statistic based on the variation matrix due to the hypothesis and the unbiased estimator of the covariance matrix. The limiting null and non-null distributions are derived as each sample size and the dimensionality go to infinity together under a general population distribution, which includes elliptical distribution with finite fourth moments or distribution assumed in Chen and Qin (2010). In two-sample case, our proposed test has the same asymptotic power as Chen and Qin (2010)’s test. In addition, it is found that our proposed test has the same asymptotic power as the one of Dempster’s trace statistic for MANOVA proposed in Fujikoshi et al. (2004) for the case that the population distributions are multivariate normal with common covariance matrix for all groups. A small scale simulation study is performed to compare the actual error probability of the first kind with the nominal.