The Cellwise Minimum Covariance Determinant Estimator

Abstract

The usual Minimum Covariance Determinant (MCD) estimator of a covariance matrix is robust against casewise outliers. These are cases (that is, rows of the data matrix) that behave differently from the majority of cases, raising suspicion that they might belong to a different population. On the other hand, cellwise outliers are individual cells in the data matrix. When a row contains one or more outlying cells, the other cells in the same row still contain useful information that we wish to preserve. We propose a cellwise robust version of the MCD method, called cellMCD. Its main building blocks are observed likelihood and a penalty term on the number of flagged cellwise outliers. It possesses good breakdown properties. We construct a fast algorithm for cellMCD based on concentration steps (C-steps) that always lower the objective. The method performs well in simulations with cellwise outliers, and has high finite-sample efficiency on clean data. It is illustrated on real data with visualizations of the results.

References in corpus (3)

• Propagation of outliers in multivariate data
• Challenges of cellwise outliers
• Robust Variable Selection under Cellwise Contamination

Cited by in corpus (7)

• Challenges of cellwise outliers
• Robust discriminant analysis
• Robust covariance estimation and explainable outlier detection for matrix-valued data
• Cellwise outlier detection in heterogeneous populations
• MacroPARAFAC for handling rowwise and cellwise outliers in incomplete multi-way data
• Comments on "Challenges of cellwise outliers" by Jakob Raymaekers and Peter J. Rousseeuw
• Robust Principal Components by Casewise and Cellwise Weighting