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

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 distri - bution 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 proce - dure using the asymptotic distribution. We also show that the proposed test proce - dure 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.