On the number of principal components in high dimensions

• 成果类型: Article
• 署名作者: Jung, Sungkyu; Lee, Myung Hee; Ahn, Jeongyoun
• 署名单位: Pennsylvania Commonwealth System of Higher Education (PCSHE); University of Pittsburgh; Cornell University; Weill Cornell Medicine; University System of Georgia; University of Georgia
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asy010
• 发表日期: 2018
• 页码: 389402
• 关键词: geometric representation; spectral projectors; sample; asymptotics; normality; CLASSIFICATION; eigenvalues; prediction; symmetry; scores

摘要

We consider how many components to retain in principal component analysis when the dimension is much higher than the number of observations. To estimate the number of components, we propose to sequentially test skewness of the squared lengths of residual scores that are obtained by removing leading principal components. The residual lengths are asymptotically left-skewed if all principal components with diverging variances are removed, and right-skewed otherwise. The proposed estimator is shown to be consistent, performs well in high-dimensional simulation studies, and provides reasonable estimates in examples.