A study of robustness for testing problem under non-normality for high-dimensional data

本文研究高维数据的统计检验问题。首先讨论了均值向量的齐性检验问题，即均值向量是否相等的检验问题。在总体服从多元正态分布的条件下，给出了检验准则。通过模拟研究，证实了当总体分布为多元t时，检验准则的精度是值得的。在含有多元正态分布的广义总体分布下，提出了另一种检验统计量。此外，我们还提出了一个检验高维数据多元正态性的检验准则。通过仿真实验，验证了当样本量和维数较大时，所提方法的精度较高。

This study is concerned with the statistical testing problem for high-dimensional data. Firstly, we dealt with the problem for testing homogeneity of mean vectors, that is, testing that all mean vectors are equal. Under the condition that the population distribution is multivariate normal, testing criterion was being proposed. Through the simulation study, I confirmed that the precision of the testing criterion gets worth when the population distribution is multivariate t. I proposed other testing statistic under a generalized population distribution which contains multivariate normal. In addition, we proposed a testing criterion for testing multivariate normality for high-dimensional data. Through simulation, we validate that the precisions of the proposals become well as the sample size and the dimension are large.