Simultaneous Inference for High-Dimensional Approximate Factor Model

This paper studies simultaneous inference for factor loadings in the approximate factor model. We propose a test statistic based on the maximum discrepancy measure. Taking advantage of the fact that the test statistic can be approximated by the sum of the independent random variables, we develop a multiplier bootstrap procedure to calculate the critical value, and demonstrate the asymptotic size and power of the test. Finally, we apply our result to multiple testing problems by controlling the family-wise error rate (FWER). The conclusions are confirmed by simulations and real data analysis.