Handling cellwise outliers by sparse regression and robust covariance

Abstract

We propose a data-analytic method for detecting cellwise outliers. Given a robust covariance matrix, outlying cells (entries) in a row are found by the cellHandler technique which combines lasso regression with a stepwise application of constructed cutoff values. The penalty term of the lasso has a physical interpretation as the total distance that suspicious cells need to move in order to bring their row into the fold. For estimating a cellwise robust covariance matrix we construct a detection-imputation method which alternates between flagging outlying cells and updating the covariance matrix as in the EM algorithm. The proposed methods are illustrated by simulations and on real data about volatile organic compounds in children.

References in corpus (2)

• Propagation of outliers in multivariate data
• Fast robust correlation for high-dimensional data

Cited by in corpus (6)

• The Cellwise Minimum Covariance Determinant Estimator
• Challenges of cellwise outliers
• Multivariate outlier explanations using Shapley values and Mahalanobis distances
• Cellwise outlier detection in heterogeneous populations
• Typical Yet Unlikely and Normally Abnormal: The Intuition Behind High-Dimensional Statistics
• Robust Principal Components by Casewise and Cellwise Weighting