# Asymptotic properties of Principal Component Analysis and shrinkage-bias adjustment under the Generalized Spiked Population model

arXiv: https://arxiv.org/abs/1607.08647 · HTML: https://mlsanity.com/paper/1607.08647/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Jul 2016.

## Built on by (most cited first, 1 of 1)

- [Double Descent: Understanding Linear Model Estimation of Nonidentifiable Parameters and a Model for Overfitting](https://mlsanity.com/paper/2408.13235/) (2024)

## Abstract (arXiv)

With the development of high-throughput technologies, principal component analysis (PCA) in the high-dimensional regime is of great interest. Most of the existing theoretical and methodological results for high-dimensional PCA are based on the spiked population model in which all the population eigenvalues are equal except for a few large ones. Due to the presence of local correlation among features, however, this assumption may not be satisfied in many real-world datasets. To address this issue, we investigated the asymptotic behaviors of PCA under the generalized spiked population model. Based on the theoretical results, we proposed a series of methods for the consistent estimation of population eigenvalues, angles between the sample and population eigenvectors, correlation coefficients between the sample and population principal component (PC) scores, and the shrinkage bias adjustment for the predicted PC scores. Using numerical experiments and real data examples from the genetics literature, we showed that our methods can greatly reduce bias and improve prediction accuracy.