PCA consistency for the power spiked model in high-dimensional settings

Authors:
Kazuyoshi Yata;Makoto Aoshima
Affiliations:
-;-
Venue:
Journal of Multivariate Analysis
Year:
2013

Citing 4
Cited 0

Eigenvalues of large sample covariance matrices of spiked population models

Journal of Multivariate Analysis
Effective PCA for high-dimension, low-sample-size data with singular value decomposition of cross data matrix

Journal of Multivariate Analysis
Effective PCA for high-dimension, low-sample-size data with noise reduction via geometric representations

Journal of Multivariate Analysis
Boundary behavior in High Dimension, Low Sample Size asymptotics of PCA

Journal of Multivariate Analysis

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Abstract

In this paper, we propose a general spiked model called the power spiked model in high-dimensional settings. We derive relations among the data dimension, the sample size and the high-dimensional noise structure. We first consider asymptotic properties of the conventional estimator of eigenvalues. We show that the estimator is affected by the high-dimensional noise structure directly, so that it becomes inconsistent. In order to overcome such difficulties in a high-dimensional situation, we develop new principal component analysis (PCA) methods called the noise-reduction methodology and the cross-data-matrix methodology under the power spiked model. We show that the new PCA methods can enjoy consistency properties not only for eigenvalues but also for PC directions and PC scores in high-dimensional settings.