A randomized test for cross-sectional correlation based on false discovery rate (FDR) control

In this paper, we introduce a multiple testing to test cross-sectional correlation based on false discovery rate (FDR) control, which addresses two primary challenges. The first is the complex dependence structure among sample correlation coefficients, which results in non-independent sub-test statistics, leading to the overall FDR being difficult to control. The second is the difficulty in computing the asymptotic variance of the sample correlation coefficient under non-normal and non-independent samples. Specifically, we propose a randomized test, wherein the individual test statistics are independent conditionally on samples. Furthermore, this method only depends on the convergence rate of the correlation coefficient rather than its asymptotic variance. We provide the asymptotic properties of the statistic under a single null and alternative hypothesis, and prove that the proposed method can control the overall FDR. In addition, the proposed method is not limited by both dimensions and models.