Augmented James--Stein estimation for leading eigenvectors and eigenspaces in high dimensions
Abstract
Building on the James--Stein approach to leading eigenvector estimation (Goldberg and Kercheval, Proc. Natl. Acad. Sci. USA 120, e2207046120, 2023), we develop a data-adaptive augmented James--Stein shrinkage framework for estimating leading eigenvectors and eigenspaces under a generalized spiked population model, in the high-dimensional regime where the dimension p and sample size n grow proportionally. For each spiked eigenvector, we construct an augmented target subspace that combines auxiliary information, either from domain knowledge or prior information, with the remaining sample spiked eigenvectors. This augmentation allows information shared across the sample spiked components to be exploited while retaining a fully data-driven shrinkage rule. We show that the resulting eigenvector estimator strictly improves upon standard PCA whenever the target subspace contains nonvanishing information about the population eigenvector, while asymptotically reverting to PCA when the target is uninformative. The individual estimators further yield a nested sequence of estimators for all leading spiked eigenspaces, with analogous dominance properties. The proposed estimator also strictly improves upon the existing HDLSS-motivated shrinkage estimator in the proportional high-dimensional regime. Simulation studies demonstrate substantial finite-sample gains and robustness to misspecification of the number of spikes.
Related
- Estimating eigenvectors and eigenspaces of covariance matrices: Optimal Bounds and Conditions for Consistency
- HEDE: Heritability estimation in high dimensions by ensembling debiased estimators in genome-wide association studies
- Keeping Score: Adaptive, Tuning-Free Loss Weighting for Score-Augmented Neural Ratio Estimation
- Orthogonal Validation-Augmented Cox Regression with Internally Validated Failure Indicators Cross-Fitted Estimation, Risk-Set Linearization, and Validation Design
- A spectral clustering-type algorithm for the consistent estimation of the Hurst distribution in moderately high dimensions
BibTeX
@misc{seong2026augmented,
title = {{Augmented James--Stein estimation for leading eigenvectors and eigenspaces in high dimensions}},
author = {Giheon Seong and Seungki Hong and Sungkyu Jung},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.34315},
eprint = {2609.34315},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.34315},
}
RIS
TY - UNPB
TI - Augmented James--Stein estimation for leading eigenvectors and eigenspaces in high dimensions
AU - Giheon Seong
AU - Seungki Hong
AU - Sungkyu Jung
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.34315
UR - https://arxiv.org/abs/2609.34315
AB - Building on the James--Stein approach to leading eigenvector estimation (Goldberg and Kercheval, Proc. Natl. Acad. Sci. USA 120, e2207046120, 2023), we develop a data-adaptive augmented James--Stein shrinkage framework for estimating leading eigenvectors and eigenspaces under a generalized spiked population model, in the high-dimensional regime where the dimension p and sample size n grow proportionally. For each spiked eigenvector, we construct an augmented target subspace that combines auxiliary information, either from domain knowledge or prior information, with the remaining sample spiked eigenvectors. This augmentation allows information shared across the sample spiked components to be exploited while retaining a fully data-driven shrinkage rule. We show that the resulting eigenvector estimator strictly improves upon standard PCA whenever the target subspace contains nonvanishing information about the population eigenvector, while asymptotically reverting to PCA when the target is uninformative. The individual estimators further yield a nested sequence of estimators for all leading spiked eigenspaces, with analogous dominance properties. The proposed estimator also strictly improves upon the existing HDLSS-motivated shrinkage estimator in the proportional high-dimensional regime. Simulation studies demonstrate substantial finite-sample gains and robustness to misspecification of the number of spikes.
ER -