Minimum covariance determinant

The minimum covariance determinant (MCD) estimator is a highly robust estimator of multivariate location and scatter. It can be computed efficiently with the FAST‐MCD algorithm of Rousseeuw and Van Driessen. Since estimating the covariance matrix is the cornerstone of many multivariate statistical methods, the MCD has also been used to develop robust and computationally efficient multivariate techniques. In this paper, we review the MCD estimator, 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 theoretical and applied multivariate statistics.