Augmented sparse principal component analysis for high dimensional data

Details Augmented sparse principal component analysis for high dimensional data Augmented sparse principal component analysis for high dimensional data

2012-02-06

arxiv.org/abs/1202.1242v1

Mathematics

Statistics Theory

This manuscript was written in 2007, and a version has been available on the first author's website, but it is posted to arXiv

Scientific paper

We study the problem of estimating the leading eigenvectors of a high-dimensional population covariance matrix based on independent Gaussian observations. We establish lower bounds on the rates of convergence of the estimators of the leading eigenvectors under $l^q$-sparsity constraints when an $l^2$ loss function is used. We also propose an estimator of the leading eigenvectors based on a coordinate selection scheme combined with PCA and show that the proposed estimator achieves the optimal rate of convergence under a sparsity regime. Moreover, we establish that under certain scenarios, the usual PCA achieves the minimax convergence rate.

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