STATISTICAL INFERENCE BASED ON ROBUST LOW-RANK DATA MATRIX APPROXIMATION

• 成果类型: Article
• 署名作者: Feng, Xingdong; He, Xuming
• 署名单位: Shanghai University of Finance & Economics; Shanghai University of Finance & Economics; University of Michigan System; University of Michigan
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/13-AOS1186
• 发表日期: 2014
• 页码: 190-210
• 关键词: least-squares; regression

摘要

The singular value decomposition is widely used to approximate data matrices with lower rank matrices. Feng and He [Ann. Appl. Stat. 3 (2009) 1634-1654] developed tests on dimensionality of the mean structure of a data matrix based on the singular value decomposition. However, the first singular values and vectors can be driven by a small number of outlying measurements. In this paper, we consider a robust alternative that moderates the effect of outliers in low-rank approximations. Under the assumption of random row effects, we provide the asymptotic representations of the robust low-rank approximation. These representations may be used in testing the adequacy of a low-rank approximation. We use oligonucleotide gene microarray data to demonstrate how robust singular value decomposition compares with the its traditional counterparts. Examples show that the robust methods often lead to a more meaningful assessment of the dimensionality of gene intensity data matrices.