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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. This article is categorized under: Statistical and Graphical Methods of Data Analysis > Multivariate Analysis Statistical and Graphical Methods of Data Analysis > Robust Methods Statistical Learning and Exploratory Methods of the Data Sciences > Knowledge Discovery [ABSTRACT FROM AUTHOR]

In this short note comments are given on the discussion paper of Cerioli, A., Riani, M., Atkinson, A. C., and Corbellini, A., entitled "The power of monitoring: How to make the most of a contaminated multivariate sample." [ABSTRACT FROM AUTHOR]

The L-median is a robust estimator of multivariate location with good statistical properties. Several algorithms for computing the L-median are available. Problem specific algorithms can be used, but also general optimization routines. The aim is to compare different algorithms with respect to their precision and runtime. This is possible because all considered algorithms have been implemented in a standardized manner in the open source environment R. In most situations, the algorithm based on the optimization routine NLM (non-linear minimization) clearly outperforms other approaches. Its low computation time makes applications for large and high-dimensional data feasible. [ABSTRACT FROM AUTHOR]