A factor-adjusted multiple testing of general alternatives

Factor-adjusted multiple testing is used for handling strong correlated tests. Since most of previous works control the false discovery rate under sparse alternatives, we develop a new method, namely the FAT-DW, for any true false proportion. In this paper, the proposed procedure is adjusted by latent factor loadings. Under the existence of explanatory variables, a uniform convergence rate of the estimated factor loadings is given. We also show that the power of FAT-DW goes to one along with the controlled false discovery rate. The performance of the proposed procedure is examined through simulations calibrated by China A-share market.