Scale-Invariant Sparse PCA on High-Dimensional Meta-Elliptical Data

• 成果类型: Article
• 署名作者: Han, Fang; Liu, Han
• 署名单位: Johns Hopkins University; Princeton University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2013.844699
• 发表日期: 2014
• 页码: 275-287
• 关键词: Principal component analysis; multivariate location; outlier detection; power method; covariance; estimators; matrix; dispersion

摘要

We propose a semiparametric method for conducting scale-invariant sparse principal component analysis (PCA) on high-dimensional non-Gaussian data. Compared with sparse PCA, our method has a weaker modeling assumption and is more robust to possible data contamination. Theoretically, the proposed method achieves a parametric rate of convergence in estimating the parameter of interests under a flexible semiparametric distribution family; computationally, the proposed method exploits a rank-based procedure and is as efficient as sparse PCA; empirically, our method outperforms most competing methods on both synthetic and real-world datasets.