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The minimum regularized covariance determinant estimator

(2020) STATISTICS AND COMPUTING. 30(1). p.113-128
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Abstract
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.

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MLA
Boudt, Kris, et al. “The Minimum Regularized Covariance Determinant Estimator.” STATISTICS AND COMPUTING, vol. 30, no. 1, 2020, pp. 113–28.
APA
Boudt, K., Rousseeuw, P. J., Vanduffel, S., & Verdonck, T. (2020). The minimum regularized covariance determinant estimator. STATISTICS AND COMPUTING, 30(1), 113–128.
Chicago author-date
Boudt, Kris, Peter J Rousseeuw, Steven Vanduffel, and Tim Verdonck. 2020. “The Minimum Regularized Covariance Determinant Estimator.” STATISTICS AND COMPUTING 30 (1): 113–28.
Chicago author-date (all authors)
Boudt, Kris, Peter J Rousseeuw, Steven Vanduffel, and Tim Verdonck. 2020. “The Minimum Regularized Covariance Determinant Estimator.” STATISTICS AND COMPUTING 30 (1): 113–128.
Vancouver
1.
Boudt K, Rousseeuw PJ, Vanduffel S, Verdonck T. The minimum regularized covariance determinant estimator. STATISTICS AND COMPUTING. 2020;30(1):113–28.
IEEE
[1]
K. Boudt, P. J. Rousseeuw, S. Vanduffel, and T. Verdonck, “The minimum regularized covariance determinant estimator,” STATISTICS AND COMPUTING, vol. 30, no. 1, pp. 113–128, 2020.
@article{8642255,
  abstract     = {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.},
  author       = {Boudt, Kris and Rousseeuw, Peter J and Vanduffel, Steven and Verdonck, Tim},
  issn         = {0960-3174},
  journal      = {STATISTICS AND COMPUTING},
  language     = {eng},
  number       = {1},
  pages        = {113--128},
  title        = {The minimum regularized covariance determinant estimator},
  url          = {http://dx.doi.org/10.1007/s11222-019-09869-x},
  volume       = {30},
  year         = {2020},
}

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