B1911
Title: Projected permutation tests for canonical correlation analysis
Authors: Yunhui Qi - Iowa State University (United States) [presenting]
Yumou Qiu - Peking University (China)
Peng Liu - Iowa State University (United States)
Abstract: Canonical correlation analysis (CCA) and sparse CCA (sCCA) are dimension-reduction tools to explore relationships between two sets of variables. An essential step in applying CCA and sCCA is to determine the number of canonical components. To do this, we sequentially test whether the remaining singular values of the cross-correlation matrix are zero, given the leading components. We call our test a projection-based permutation test (PPT) because we use projection to exclude the information carried by leading components and use permutation to test whether there exists information in the remaining components. In high dimensions, we further propose to use a low-dimensional transformation to amplify signals. Our method overcomes the shadowing problem of parallel analysis by projection, thus having higher power. It is also more robust to the accuracy of sCCA, reducing the requirements of penalty parameters. In addition, we propose a procedure to test if the loadings are zero, which helps select the contributing variables. Simulation studies show our methods have lower error rates and higher power compared to the existing ones. A case study on COVID patients reveals the connection between COVID severity and the functions of proteome and metabolome.
