An alternative bootstrap procedure for factor-augmented regression models

2025-10-01

AI Summary

Existing bootstrap methods for factor-augmented regression suffer from low distributional approximation efficiency when rotating parameter vectors and exhibit substantial bias and slow convergence under weak-factor panel settings. To address these issues, this paper proposes a novel, computationally efficient bootstrap procedure. The method innovatively introduces two data-dependent rotation matrices and a unique signal-dependent population counterpart matrix, substantially reducing asymptotic bias and accelerating convergence in weak-factor regimes. Theoretically, we establish the asymptotic validity of the estimator within a weak-factor framework where eigenvalues diverge at heterogeneous rates, integrating principal component analysis with factor extraction. Empirically, the proposed algorithm demonstrates markedly superior finite-sample inference accuracy and stability compared to conventional bootstrap approaches—particularly in large-scale panel datasets featuring multiple weak factors.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

In this paper, we propose a novel bootstrap algorithm that is more efficient than existing methods for approximating the distribution of the factor-augmented regression estimator for a rotated parameter vector. The regression is augmented by $r$ factors extracted from a large panel of $N$ variables observed over $T$ time periods. We consider general weak factor (WF) models with $r$ signal eigenvalues that may diverge at different rates, $N^{α_{k}}$, where $0<α_{k}leq 1$ for $k=1,2,...,r$. We establish the asymptotic validity of our bootstrap method using not only the conventional data-dependent rotation matrix $hat{H}$, but also an alternative data-dependent rotation matrix, $hat{H}_q$, which typically exhibits smaller asymptotic bias and achieves a faster convergence rate. Furthermore, we demonstrate the asymptotic validity of the bootstrap under a purely signal-dependent rotation matrix ${H}$, which is unique and can be regarded as the population analogue of both $hat{H}$ and $hat{H}_q$. Experimental results provide compelling evidence that the proposed bootstrap procedure achieves superior performance relative to the existing procedure.

Problem

• Developing efficient bootstrap for factor-augmented regression models
• Addressing weak factor models with divergent eigenvalue rates
• Validating bootstrap under different rotation matrix specifications

Innovation

• Novel bootstrap algorithm for factor-augmented regression models
• Uses alternative rotation matrix with reduced asymptotic bias
• Validates bootstrap under signal-dependent population rotation matrix