Multivariate location and scatter matrix estimation under cellwise and casewise contamination

Andy Leung, Victor Yohai and Ruben Zamar

Computational Statistics & Data Analysis, 2017, vol. 111, issue C, 59-76

Abstract: Real data may contain both cellwise outliers and casewise outliers. There is a vast literature on robust estimation for casewise outliers, but only a scant literature for cellwise outliers and almost none for both types of outliers. Estimation of multivariate location and scatter matrix is a corner stone in multivariate data analysis. A two-step approach was recently proposed to perform robust estimation of multivariate location and scatter matrix in the presence of cellwise and casewise outliers. In the first step a univariate filter was applied to remove cellwise outliers. In the second step a generalized S-estimator was used to downweight casewise outliers. This proposal can be further improved in three main directions. First, through the introduction of a consistent bivariate filter to be used in combination with the univariate filter in the first step. Second, through the proposal of a new fast subsampling procedure to generate starting points for the generalized S-estimator in the second step. Third, through the use of a non-monotonic weight function for the generalized S-estimator to better handle casewise outliers in high dimension. A simulation study and a real data example show that, unlike the original two-step procedure, the modified two-step approach performs and scales well in high dimension. Moreover, they show that the modified procedure outperforms the original one and other state-of-the-art robust procedures under cellwise and casewise data contamination.

Keywords: Multivariate location and scatter; Robust estimation; Cellwise outliers; Componentwise contamination (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:111:y:2017:i:c:p:59-76

DOI: 10.1016/j.csda.2017.02.007

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