论文标题
限制与WishArt矩阵相关的定理，并应用于普通主要组件的假设测试
Limit theorem associated with Wishart matrices with application to hypothesis testing for common principal components
论文作者
论文摘要
当自由度的程度和分布的矩阵参数的大小同时增长时，这项研究将获得Wishart分布的新特性。特别是，在高维渐近方面显示了四个独立的Wishart矩阵产物的渐近正态性。作为结果的应用，提出了针对普通主成分假设的统计测试程序。对于此问题，在零假设下，提出的测试统计量渐近地正常。此外，在替代假设下，拟议的测试统计量在概率上与阳性无穷大。
This study derives a new property of the Wishart distribution when the degree-of-freedom and the size of the matrix parameter of the distribution grow simultaneoulsy. Particularly, the asymptotic normality of the product of four independent Wishart matrices is shown under a high dimensional asymptotic regime. As an application of the result, a statistical test procedure for the common principal components hypothesis is proposed. For this problem, the proposed test statistic is asymptotically normal under the null hypothesis. In addition, the proposed test statistic diverges to positive infinity in probability under the alternative hypothesis.
