Electronic Journal of Statistics

High dimension low sample size asymptotics of robust PCA

Yi-Hui Zhou and J. S. Marron

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Abstract

Conventional principal component analysis is highly susceptible to outliers. In particular, a sufficiently outlying single data point, can draw the leading principal component toward itself. In this paper, we study the effects of outliers for high dimension and low sample size data, using asymptotics. The non-robust nature of conventional principal component analysis is verified through inconsistency under multivariate Gaussian assumptions with a single spike in the covariance structure, in the presence of a contaminating outlier. In the same setting, the robust method of spherical principal components is consistent with the population eigenvector for the spike model, even in the presence of contamination.

Article information

Source
Electron. J. Statist., Volume 9, Number 1 (2015), 204-218.

Dates
First available in Project Euclid: 9 February 2015

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1423491229

Digital Object Identifier
doi:10.1214/15-EJS992

Mathematical Reviews number (MathSciNet)
MR3312407

Zentralblatt MATH identifier
1307.62160

Keywords
Outlier robustness spherical PCA spike model

Citation

Zhou, Yi-Hui; Marron, J. S. High dimension low sample size asymptotics of robust PCA. Electron. J. Statist. 9 (2015), no. 1, 204--218. doi:10.1214/15-EJS992. https://projecteuclid.org/euclid.ejs/1423491229


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