TY - JOUR

T1 - The minimum regularized covariance determinant estimator

AU - Boudt, Kris

AU - Rousseeuw, Peter J.

AU - Vanduffel, Steven

AU - Verdonck, Tim

PY - 2020/2

Y1 - 2020/2

N2 - The minimum covariance determinant (MCD) approach estimates the location and scatter matrix using the subset of given size with lowest sample covariance determinant. Its main drawback is that it cannot be applied when the dimension exceeds the subset size. We propose the minimum regularized covariance determinant (MRCD) approach, which differs from the MCD in that the scatter matrix is a convex combination of a target matrix and the sample covariance matrix of the subset. A data-driven procedure sets the weight of the target matrix, so that the regularization is only used when needed. The MRCD estimator is defined in any dimension, is well-conditioned by construction and preserves the good robustness properties of the MCD. We prove that so-called concentration steps can be performed to reduce the MRCD objective function, and we exploit this fact to construct a fast algorithm. We verify the accuracy and robustness of the MRCD estimator in a simulation study and illustrate its practical use for outlier detection and regression analysis on real-life high-dimensional data sets in chemistry and criminology.

AB - The minimum covariance determinant (MCD) approach estimates the location and scatter matrix using the subset of given size with lowest sample covariance determinant. Its main drawback is that it cannot be applied when the dimension exceeds the subset size. We propose the minimum regularized covariance determinant (MRCD) approach, which differs from the MCD in that the scatter matrix is a convex combination of a target matrix and the sample covariance matrix of the subset. A data-driven procedure sets the weight of the target matrix, so that the regularization is only used when needed. The MRCD estimator is defined in any dimension, is well-conditioned by construction and preserves the good robustness properties of the MCD. We prove that so-called concentration steps can be performed to reduce the MRCD objective function, and we exploit this fact to construct a fast algorithm. We verify the accuracy and robustness of the MRCD estimator in a simulation study and illustrate its practical use for outlier detection and regression analysis on real-life high-dimensional data sets in chemistry and criminology.

KW - Breakdown value

KW - High-dimensional data

KW - Regularization

KW - Robust covariance estimation

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U2 - 10.1007/s11222-019-09869-x

DO - 10.1007/s11222-019-09869-x

M3 - Article

AN - SCOPUS:85064342827

VL - 30

SP - 113

EP - 128

JO - Statistics and Computing

JF - Statistics and Computing

SN - 0960-3174

IS - 1

ER -