統計数学セミナー
Seminar on Probability and Statistics
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Seminar on Probability and Statistics
Friday November 30 2012
Tokyo 006
2:50-4:00 pm


Effective PCA for high-dimensional, non-Gaussian data under power spiked model


矢田 和善 / YATA, Kazuyoshi
筑波大学 数理物質科学研究科 / Institute of Mathematics, University of Tsukuba

Abstract

In this talk, we introduce a general spiked model called the power spiked model in high-dimensional settings. We first consider asymptotic properties of the conventional estimator of eigenvalues under the power spiked model. We give several conditions on the dimension $p$, the sample size $n$ and the high-dimensional noise structure in order to hold several consistency properties of the estimator. We show that the estimator is affected by the noise structure, directly, so that the estimator becomes inconsistent for such cases. In order to overcome such difficulties in a high-dimensional situation, we develop new PCAs called the noise-reduction methodology and the cross-data-matrix methodology under the power spiked model. This is a joint work with Prof. Aoshima (University of Tsukuba).




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Seminar on Probability and Statistics