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February 2014 Statistical inference based on robust low-rank data matrix approximation
Xingdong Feng, Xuming He
Ann. Statist. 42(1): 190-210 (February 2014). DOI: 10.1214/13-AOS1186

Abstract

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.

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Xingdong Feng. Xuming He. "Statistical inference based on robust low-rank data matrix approximation." Ann. Statist. 42 (1) 190 - 210, February 2014. https://doi.org/10.1214/13-AOS1186

Information

Published: February 2014
First available in Project Euclid: 18 February 2014

zbMATH: 1302.62068
MathSciNet: MR3178461
Digital Object Identifier: 10.1214/13-AOS1186

Subjects:
Primary: 62F03 , 62F35
Secondary: 62F05 , 62F10 , 62F12

Keywords: Hypothesis testing , M estimator , Singular value decomposition , trimmed least squares

Rights: Copyright © 2014 Institute of Mathematical Statistics

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Vol.42 • No. 1 • February 2014
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