Some high-dimensional tests for a one-way MANOVA
Some high-dimensional tests for a one-way MANOVA
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DOI：
10.1016/j.jmva.2006.11.007
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发表时间：
2007-10-01
影响因子：
1.6
通讯作者：
Schott, James R.
中科院分区：
文献类型：
--
作者：
Schott, James R.
提出了一种检验单向多元方差分析中均值向量相等性的统计量。当样本大小和变量数目都趋于无穷大时，该统计量的渐近零分布是正态分布。因此，当变量的数量相对于样本大小不小时，可以使用该检验。特别是，当变量的数量超过误差自由度时，可以使用它，在这种情况下，标准的马诺瓦检验是无效的。发展了一个相关的统计量，该统计量也具有渐近正态分布，用于检验由总体平均向量形成的超平面的维度。通过仿真研究，评估了正态近似的有限样本量性能。
A statistic is proposed for testing the equality of the mean vectors in a one-way multivariate analysis of variance. The asymptotic null distribution of this statistic, as both the sample size and the number of variables go to infinity, is shown to be normal. Thus, this test can be used when the number of variables is not small relative to the sample size. In particular, it can be used when the number of variables exceeds the degrees of freedom for error, a situation in which standard MANOVA tests are invalid. A related statistic, also having an asymptotic normal distribution, is developed for tests concerning the dimensionality of the hyperplane formed by the population mean vectors. The finite sample size performances of the normal approximations are evaluated in a simulation study.