Cell-wise robust covariance estimation for compositions, with application to geochemical data

Abstract

Cell-wise outliers are outliers in single entries of a compositional data matrix, and they can lead to a certain bias in the statistical analysis. Traditional row-wise robust methods downweight outlying observations for the estimation, independent of how many or which cells of an observation are contaminated. Cell-wise robustness still makes use of the information contained in non-contaminated cells. Here, cell-wise robustness is used for the estimation of the variation and the covariance matrix. For higher dimensional data also a regularized estimator is introduced. The advantages of the cell-wise robust estimators are demonstrated in simulation experiments and in a geochemistry application in the context of clustering and principal component analysis.