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In this paper, we develop bootstrap methods for factor-augmented regressions with potentially weak common components, allowing signal eigenvalues to diverge at heterogeneous rates $N^{α_k}$, where $0<α_k\leq1$, $k=1,\ldots,r$. The regression estimator targets a rotation of the latent parameter vector that may be data dependent, while factor estimation can induce asymptotic bias. The proposed procedure directly constructs the rotation-specific target in the bootstrap world,…

重审近似因子模型主成分估计量的渐近理论AI 解读

It is well known that approximate factor models exhibit rotation indeterminacy. Principal component (PC) estimators are typically analyzed relative to a rotated factor-loading representation, but the commonly used rotation depends on the estimator itself, leaving unclear which fixed population parameters are estimated. We show that any starting representation of the common component can be mapped by a rotation matrix $\bH$, constructed without using the PC estimator or the…

弱因子下因子增强回归模型的偏差修正AI 解读

In this paper, we study the asymptotic bias of the factor-augmented regression estimator and its reduction, which is augmented by the $r$ factors extracted from a large number of $N$ variables with $T$ observations. In particular, we consider general weak latent factor models with $r$ signal eigenvalues that may diverge at different rates, $N^{α_{k}}$, $0<α_{k}\leq 1$, $k=1,\dots,r$. In the existing literature, the bias has been derived using an approximation for the…