著者

Yata Kazuyoshi Aoshima Makoto

出版者

Elsevier

雑誌

Journal of multivariate analysis (ISSN:0047259X)

巻号頁・発行日

vol.122, pp.334-354, 2013-11

被引用文献数

20

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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.

著者

Yata Kazuyoshi Aoshima Makoto

出版者

Elsevier

雑誌

Journal of multivariate analysis (ISSN:0047259X)

巻号頁・発行日

vol.117, pp.313-331, 2013-05

被引用文献数

17

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In this paper, we consider tests of correlation when the sample size is much lower than the dimension. We propose a new estimation methodology called the extended cross-data-matrix methodology. By applying the method, we give a new test statistic for high-dimensional correlations. We show that the test statistic is asymptotically normal when p→∞p→∞ and n→∞n→∞. We propose a test procedure along with sample size determination to ensure both prespecified size and power for testing high-dimensional correlations. We further develop a multiple testing procedure to control both family wise error rate and power. Finally, we demonstrate how the test procedures perform in actual data analyses by using two microarray data sets.