A simple test for zero multiple correlation coefficient in high-dimensional normal data using random projection

Abstract

The multiple correlation coefficient (MCC) is a measure of linear relationship between a given variable and a set of covariates. Testing the hypothesis of zero MCC has always been important in multiple correlation analysis. For testing this hypothesis, due to the singularity of the sample covariance matrix in high-dimensional data, the classical testing procedures are no longer usable. To test the null hypothesis of zero MCC in high-dimensional normal data, a simple testing procedure is proposed by using the random projection and union-intersection methodologies. Some simulations are carried out to verify the performance evaluation of the proposed test. The results are found to be very convincing. In the end, the experimental validation of the proposed test is carried out on mice tumor data.