Bootstrap correction for bias from using estimated residuals in high-dimensional factor models

Develop bootstrap procedures that correct the bias arising from using cross-sectional OLS residual estimates rather than the true residuals in high-dimensional factor models and yield valid finite-sample inferential guarantees for test statistics assessing independence of asset-specific residual time series when the number of factors k is non-negligible relative to the number of assets p.

Background

The paper highlights that in the factor-model setting with known exposures, hypothesis testing relies on estimated residuals obtained from cross-sectional OLS projections. Even under the null of independent residual processes, the covariance of the estimated residuals differs from that of the true residuals because projection matrices induce cross-sectional dependence; this discrepancy does not vanish when the number of factors is not negligible relative to the number of assets.

The authors note that while high-dimensional bootstrap methods exist for maxima of sums, their setting introduces additional bias due to using estimated residuals, and it is unclear how to correct this bias with bootstrap. They therefore present a nonparametric mosaic permutation test as an alternative but explicitly flag the bootstrap correction as an unresolved issue.