A refined bootstrap procedure for high‐dimensional factor‐augmented regression models

In this paper, we address the adequacy testing problem for high‐dimensional factor‐augmented regression models. Existing methods often require the estimation of high‐dimensional precision matrices or regression coefficients, resulting in significant computational complexity. To overcome this challenge, we refine the bootstrap testing procedure based on the maximum‐type test statistic of the estimated score function as introduced by Beyhum and Striaukas (2024b). Our method avoids the estimation of both precision matrices and high‐dimensional regression coefficients, thereby substantially reducing computational complexity and simplifying implementation. Theoretically, we establish the validity of the proposed procedure under the null hypothesis and demonstrate its power to detect signals under suitable conditions. We demonstrate the finite‐sample performance of the proposed method through comprehensive simulations and an empirical illustration using a macroeconomic dataset.