Biometrika Dec 26, 2025

Estimating the number of significant components in high-dimensional PCA

Authors
Bo Zhang Guangming Pan ZhiXiang Zhang
Research Topics
High-Dimensional Statistics
Paper Information
  • Journal:
    Biometrika
  • DOI:
    10.1093/biomet/asaf092
  • Published:
    December 26, 2025
  • Added to Tracker:
    Feb 10, 2026
Abstract

SUMMARY We consider the problem of estimating the number of significant components in high-dimensional principal component analysis (pca). We propose a new penalized approach using the explained variance ratio and the rigidity of the nonspiked sample eigenvalues of sample covariance matrices of p variables. Compared with the existing literature, the consistency of the estimator holds not only for independent data but also for some times series data when the dimension p and the sample size n both tend to infinity. Even for independent data it works under weaker conditions including allowing the heterogeneity in the bulk of the population eigenvalues than the existing approaches such as aic and bic. Simulation studies are also conducted to illustrate its good performance.

Author Details
Bo Zhang
Author
Guangming Pan
Author
ZhiXiang Zhang
Author
Research Topics & Keywords
High-Dimensional Statistics
Research Area
Citation Information
APA Format
Bo Zhang , Guangming Pan & ZhiXiang Zhang (2025) . Estimating the number of significant components in high-dimensional PCA. Biometrika , 10.1093/biomet/asaf092.
BibTeX Format
@article{paper869,
  title = { Estimating the number of significant components in high-dimensional PCA },
  author = { Bo Zhang and Guangming Pan and ZhiXiang Zhang },
  journal = { Biometrika },
  year = { 2025 },
  doi = { 10.1093/biomet/asaf092 },
  url = { https://doi.org/10.1093/biomet/asaf092 }
}