A0552
Title: New tests for high-dimensional two-sample mean problems with consideration of correlation structure
Authors: Songshan Yang - Renmin University of China (China) [presenting]
Abstract: A test statistic is proposed for two sample mean testing problems for high dimensional data by assuming the linear structure on high dimensional precision matrices. A new precision matrix estimation method considering its linear structure is first proposed, and the regularization method is implemented to select the true basis matrices that can further reduce the approximation error. Then the test statistic is constructed by imposing the estimation of the precision matrix. The proposed test is valid for both the low- and high-dimensional settings, even if the dimension of the data is greater than the sample size. The limiting null distributions of the proposed test statistic are derived under both null and alternative distributions. Extensive simulations are conducted to estimate the precision matrix and test the difference of the high-dimensional mean vector. Simulation results show that the proposed estimation method enjoys low estimation error for the precision matrix, and the regularization method is able to select the important basis matrix efficiently. The testing method performs well compared to existing methods, especially when the vector elements have unequal variances. A real data example is then provided to demonstrate the potential of the proposed method in real-world applications.
