SELECTING THE NUMBER OF PRINCIPAL COMPONENTS: ESTIMATION OF THE TRUE RANK OF A NOISY MATRIX

• 成果类型: Article
• 署名作者: Choi, Yunjin; Taylor, Jonathan; Tibshirani, Robert
• 署名单位: National University of Singapore; Stanford University; Stanford University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/16-AOS1536
• 发表日期: 2017
• 页码: 2590-2617
• 关键词: regression

摘要

Principal component analysis (PCA) is a well-known tool in multivariate statistics. One significant challenge in using PCA is the choice of the number of principal components. In order to address this challenge, we propose distribution-based methods with exact type 1 error controls for hypothesis testing and construction of confidence intervals for signals in a noisy matrix with finite samples. Assuming Gaussian noise, we derive exact type 1 error controls based on the conditional distribution of the singular values of a Gaussian matrix by utilizing a post-selection inference framework, and extending the approach of [Taylor, Loftus and Tibshirani (2013)] in a PCA setting. In simulation studies, we find that our proposed methods compare well to existing approaches.