CONVERGENCE AND PREDICTION OF PRINCIPAL COMPONENT SCORES IN HIGH-DIMENSIONAL SETTINGS.
CONVERGENCE AND PREDICTION OF PRINCIPAL COMPONENT SCORES IN HIGH-DIMENSIONAL SETTINGS.
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DOI：
10.1214/10-aos821
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发表时间：
2010-01-01
影响因子：
4.5
通讯作者：
Wright FA
中科院分区：
文献类型：
--
作者：
Lee S;Zou F;Wright FA
出现了许多设置，其中感兴趣的是使用来自初始样本的数据来预测新观测的主成分（PC）得分。在本文中，我们证明了PC分数预测的天真方法可以在大矩阵分析中基本上偏向于0。这种现象在很大程度上与已知的样本特征值和特征向量的不一致结果有关，因为矩阵的两个维度都增加了。对于随机矩阵的尖峰特征值模型，我们扩展了这些结果的一般性，并提出了偏差调整的PC得分预测。此外，我们还计算了样本PC得分与总体特征向量之间的渐近相关系数。遗传学文献的模拟和真实的数据例子表明，我们的估计改进的偏差和数值特性。
A number of settings arise in which it is of interest to predict Principal Component (PC) scores for new observations using data from an initial sample. In this paper, we demonstrate that naive approaches to PC score prediction can be substantially biased towards 0 in the analysis of large matrices. This phenomenon is largely related to known inconsistency results for sample eigenvalues and eigenvectors as both dimensions of the matrix increase. For the spiked eigenvalue model for random matrices, we expand the generality of these results, and propose bias-adjusted PC score prediction. In addition, we compute the asymptotic correlation coefficient between PC scores from sample and population eigenvectors. Simulation and real data examples from the genetics literature show the improved bias and numerical properties of our estimators.