PCA consistency for the power spiked model in high-dimensional settings
PCA consistency for the power spiked model in high-dimensional settings
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DOI：
10.1016/j.jmva.2013.08.003
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发表时间：
2013-11
期刊：
影响因子：
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通讯作者：
K. Yata;M. Aoshima
中科院分区：
文献类型：
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作者：
K. Yata;M. Aoshima
在本文中，我们提出了高维环境下的一般尖刺模型，称为功率尖刺模型。导出了数据维数、样本大小和高维噪声结构之间的关系。我们首先考虑特征值的常规估计量的渐近性质。研究表明，估计量受到高维噪声结构的直接影响，使估计量变得不一致。为了克服在高维情况下的这些困难，我们开发了新的主成分分析（PCA）方法，即功率尖峰模型下的降噪方法和交叉数据矩阵方法。我们证明了新的PCA方法不仅对特征值具有一致性，而且对高维环境下的PC方向和PC分数也具有一致性。
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.