This paper proposes and theoretically justifies bootstrap methods for regressions where some of the regressors are factors estimated from a large panel of data. We derive our results under the assumption that root T/N -> c, where 0 <= c < infinity (N and T are the cross-sectional and the time series dimensions, respectively), thus allowing for the possibility that the factor estimation error enters the limiting distribution of the OLS estimator as an asymptotic bias term (as was recently discussed by Ludvigson and Ng (2011)). We consider general residual-based bootstrap methods and provide a set of high-level conditions on the bootstrap residuals and on the idiosyncratic errors such that the bootstrap distribution of a rotated OLS estimator is consistent. We subsequently verify these conditions for a simple wild bootstrap residual-based procedure
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机译：本文提出了bootstrap方法，并从理论上证明了回归的bootstrap方法，其中一些回归因子是从大量数据中估计的因子。我们在假设根T / N-> c的情况下得出我们的结果，其中0 <= c <无穷大（N和T分别是横截面和时间序列维），因此考虑了因子估计的可能性误差作为渐近偏差项进入OLS估计的极限分布（最近由Ludvigson和Ng（2011）讨论）。我们考虑一般的基于残差的自举方法，并提供有关自举残差和特异误差的一组高级条件，以使旋转的OLS估计量的自举分布保持一致。我们随后验证了这些条件，以进行基于残差的简单自举程序
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