arXiv subjects

Peiyun Jiang

Publications and source records attributed to Peiyun Jiang.

3 recordsLinked to original sources

arXiv2026

Revisiting Asymptotic Theory for Principal Component Estimators of Approximate Factor Models

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 idiosyncratic errors and unique up to column signs, to a population representation satisfying the same PC normalization as the estimator. Although $\bH$ depends on the starting representation, the resulting representation is invariant to that choice up to simultaneous column sign changes. We call the resulting factors and loadings the pseudo-true (PC-normalized) parameters. Under a general weak factor model allowing signal eigenvalues to diverge at possibly different rates, we establish consistency and asymptotic normality of the PC estimators for these fixed, estimator-independent targets, together with fixed-target asymptotic theory for factor-augmented regressions. The theory thereby justifies confidence intervals for PC-normalized factors, gives loading profiles a fixed-target interpretation, and identifies the population coefficients associated with estimated PC factors in factor-augmented regressions.

math.ST↗

arXiv2025

Bias Correction in Factor-Augmented Regression Models with Weak Factors

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 estimated factors with a specific data-dependent rotation matrix $\hat{H}$ for the model with $α_{k}=1$ for all $k$, whereas we derive the bias for weak factor models. In addition, we derive the bias using the approximation with a different rotation matrix $\hat{H}_q$, which generally has a smaller bias than with $\hat{H}$. We also derive the bias using our preferred approximation with a purely signal-dependent rotation $H$, which is unique and can be regarded as the population version of $\hat{H}$ and $\hat{H}_q$. Since this bias is parametrically inestimable, we propose a split-panel jackknife bias correction, and theory shows that it successfully reduces the bias. The extensive finite-sample experiments suggest that the proposed bias correction works very well, and the empirical application illustrates its usefulness in practice.

stat.ME↗

arXiv2025

An alternative bootstrap procedure for factor-augmented regression models

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 $\hat{\bH}$, but also an alternative data-dependent rotation matrix, $\hat{\bH}_q$, 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 ${\bH}$, which is unique and can be regarded as the population analogue of both $\hat{\bH}$ and $\hat{\bH}_q$. Experimental results provide compelling evidence that the proposed bootstrap procedure achieves superior performance relative to the existing procedure.

stat.ME↗