论文标题
使用随机投影在高维度中的协方差矩阵测试
Covariance matrix testing in high dimension using random projections
论文作者
论文摘要
高维度中协方差矩阵的估计和假设检验是一个具有挑战性的问题，因为传统的多元渐近理论不再有效。当尺寸大于样本量大或增加时，基于标准可能性的协方差矩阵测试的性能较差。现有的高维测试在计算上是昂贵的，或者对I型错误的控制非常弱。在本文中，我们提出了一种测试程序，用于测试使用随机预测的一个或多个协方差矩阵的假设。将高维数据随机投影到较低的尺寸子空间减轻维度的诅咒，从而允许使用传统的多元测试。进行了广泛的仿真研究，以将抽筋与基于渐近药的高维测试程序进行比较。提出了该方法在两个基因表达数据集中的应用。
Estimation and hypothesis tests for the covariance matrix in high dimensions is a challenging problem as the traditional multivariate asymptotic theory is no longer valid. When the dimension is larger than or increasing with the sample size, standard likelihood based tests for the covariance matrix have poor performance. Existing high dimensional tests are either computationally expensive or have very weak control of type I error. In this paper, we propose a test procedure, CRAMP, for testing hypotheses involving one or more covariance matrices using random projections. Projecting the high dimensional data randomly into lower dimensional subspaces alleviates of the curse of dimensionality, allowing for the use of traditional multivariate tests. An extensive simulation study is performed to compare CRAMP against asymptotics-based high dimensional test procedures. An application of the proposed method to two gene expression data sets is presented.
