AFSR: An Adaptive Factor Score Regression Framework for High‐Dimensional Correlation Matrix Estimation

The accurate estimation of correlation matrices is a foundational challenge in high‐dimensional statistics. The sample correlation matrix, while unbiased, suffers from high variance when the number of variables p is large relative to the sample size n , leading to unstable estimates and poor performance in downstream applications. This paper introduces the adaptive factor‐informed shrinkage regression (AFSR) framework, a novel methodology that moves beyond the traditional binary choice between the noisy sample matrix and potentially biased structured estimators. The AFSR estimator is defined as a convex combination of the sample correlation matrix and a low‐rank factor‐informed target, forming a continuum of estimators that accommodates both exact and approximate factor model assumptions. The key innovation is a cross‐validation procedure to select the optimal shrinkage intensity, effectively approximating the oracle estimator that minimizes the mean squared error. Connections to Ridge‐type shrinkage, Ledoit–Wolf methods, POET, and nuclear‐norm regularization are discussed, positioning AFSR within the broader landscape of regularization approaches. We demonstrate that this adaptive approach consistently outperforms established benchmarks, including the sample matrix, the model‐implied factor analysis matrix, Ledoit–Wolf shrinkage, POET, and graphical lasso, across a wide range of high‐dimensional simulation scenarios. The practical utility of the AFSR framework is further validated through applications to real‐world datasets from genomics and finance, showcasing its robustness to non‐normality and automatic adaptability to underlying data structures.