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Robust Low-Rank Approximation of Data Matrices With Elementwise Contamination

Summary: [This abstract is based on the authors' abstract.] A robust method based on Yohai’s regression MM estimates is proposed to approximate an n x p data matrix with one rank of q. Its purpose is to be resistant to the presence of atypical rows and scattered atypical cells, and to also cope with missing values. In addition, an algorithm is proposed based on alternating M-regressions and a starting estimate based on successive rank-one fits. The proposed estimate is demonstrated on three high-dimensional data sets and is shown to outperform competing estimates in terms of efficiency and resistance.

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  • Topics: Data Quality
  • Keywords: Regression analysis, Outliers, Multivariate, Principal components
  • Author: Maronna, Ricardo A.; Yohai, Victor J.
  • Journal: Technometrics