The Annals of Statistics

Convergence and prediction of principal component scores in high-dimensional settings

Seunggeun Lee, Fei Zou, and Fred A. Wright

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A number of settings arise in which it is of interest to predict Principal Component (PC) scores for new observations using data from an initial sample. In this paper, we demonstrate that naive approaches to PC score prediction can be substantially biased toward 0 in the analysis of large matrices. This phenomenon is largely related to known inconsistency results for sample eigenvalues and eigenvectors as both dimensions of the matrix increase. For the spiked eigenvalue model for random matrices, we expand the generality of these results, and propose bias-adjusted PC score prediction. In addition, we compute the asymptotic correlation coefficient between PC scores from sample and population eigenvectors. Simulation and real data examples from the genetics literature show the improved bias and numerical properties of our estimators.

Article information

Ann. Statist. Volume 38, Number 6 (2010), 3605-3629.

First available in Project Euclid: 30 November 2010

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62H25: Factor analysis and principal components; correspondence analysis
Secondary: 15A18: Eigenvalues, singular values, and eigenvectors

PCA PC scores random matrix PC regression


Lee, Seunggeun; Zou, Fei; Wright, Fred A. Convergence and prediction of principal component scores in high-dimensional settings. Ann. Statist. 38 (2010), no. 6, 3605--3629. doi:10.1214/10-AOS821.

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