Correlation tests for high-dimensional data under the strongly spiked eigenvalue model

Abstract Correlation tests are very important tools for the pathway analysis or graphical modeling of high-dimensional data. In this study, we consider a correlation test under the strongly spiked eigenvalue (SSE) model in high-dimension, low-sample-size scenarios, where the sample size is much smaller than the dimension. High-dimensional data often fit the SSE model. Previously, a high-dimensional test for a correlation matrix under the non-SSE model was constructed using the extended cross-data-matrix (ECDM) methodology. Here, we show that an asymptotic distribution of the test statistic using ECDM methodology under the SSE model can be written using the distribution of the sum of some weighted chi-squared variables when both dimension and sample size reach infinity. We propose a new test procedure using the asymptotic distribution. We also show that the proposed test procedure has preferable properties for power and size. We discuss the performance of the test procedure through simulations and present a demonstration with actual data analyses using a microarray data set.