Estimating the number of significant components in high-dimensional PCA
Authors
Research Topics
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
AuthorGuangming Pan
AuthorZhiXiang Zhang
AuthorResearch Topics & Keywords
High-Dimensional Statistics
Research AreaCitation 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 }
}