Minimum Covariance Determinant and Extensions

Abstract

The Minimum Covariance Determinant (MCD) method is a highly robust estimator of multivariate location and scatter, for which a fast algorithm is available. Since estimating the covariance matrix is the cornerstone of many multivariate statistical methods, the MCD is an important building block when developing robust multivariate techniques. It also serves as a convenient and efficient tool for outlier detection. The MCD estimator is reviewed, along with its main properties such as affine equivariance, breakdown value, and influence function. We discuss its computation, and list applications and extensions of the MCD in applied and methodological multivariate statistics. Two recent extensions of the MCD are described. The first one is a fast deterministic algorithm which inherits the robustness of the MCD while being almost affine equivariant. The second is tailored to high-dimensional data, possibly with more dimensions than cases, and incorporates regularization to prevent singular matrices.

References in corpus (4)

• High-Breakdown Robust Multivariate Methods
• A robust method for cluster analysis
• Central limit theorem and influence function for the MCD estimators at general multivariate distributions
• Econometric applications of high-breakdown robust regression techniques

Cited by in corpus (12)

• Constraining the Milky Way Mass Profile with Phase-Space Distribution of Satellite Galaxies
• Negative Selection Algorithm Research and Applications in the last decade: A Review
• The Cellwise Minimum Covariance Determinant Estimator
• Outlier detection in non-elliptical data by kernel MRCD
• Real-time outlier detection for large datasets by RT-DetMCD
• A robust approach to model-based classification based on trimming and constraints
• Robust discriminant analysis
• Machine learning approach to stock price crash risk
• Tandem clustering with invariant coordinate selection
• MacroPARAFAC for handling rowwise and cellwise outliers in incomplete multi-way data
• A Two-Stage Bayesian Semiparametric Model for Novelty Detection with Robust Prior Information
• SPINEX: Similarity-based Predictions with Explainable Neighbors Exploration for Anomaly and Outlier Detection