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The Minimum Regularized Covariance Determinant Estimator

25 Pages Posted: 3 Feb 2017  

Kris Boudt

Vrije Universiteit Brussel (VUB); VU University Amsterdam

Peter Rousseeuw

KU Leuven - Department of Mathematics

Steven Vanduffel

Vrije Universiteit Brussel (VUB)

Tim Verdonck

Department of Mathematics, KU Leuven

Date Written: January 24, 2017

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 subset-based covariance matrix is a convex combination of a target matrix and the sample covariance matrix. 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.

Keywords: Breakdown point, High-dimensional data, Regularization, Robust covariance estimation

JEL Classification: C14, C32

Suggested Citation

Boudt, Kris and Rousseeuw, Peter and Vanduffel, Steven and Verdonck, Tim, The Minimum Regularized Covariance Determinant Estimator (January 24, 2017). Available at SSRN: https://ssrn.com/abstract=2905259

Kris Boudt (Contact Author)

Vrije Universiteit Brussel (VUB) ( email )

Pleinlaan 2
http://www.vub.ac.be/
Brussels, 1050
Belgium

VU University Amsterdam ( email )

De Boelelaan 1105
Amsterdam, ND North Holland 1081 HV
Netherlands

Peter Rousseeuw

KU Leuven - Department of Mathematics ( email )

Celestijnenlaan 200 B
Leuven, B-3001
Belgium

Steven Vanduffel

Vrije Universiteit Brussel (VUB) ( email )

Pleinlaan 2
Brussels, Brabant 1050
Belgium

HOME PAGE: http://www.stevenvanduffel.com

Tim Verdonck

Department of Mathematics, KU Leuven ( email )

Celestijnenlaan 200B
Leuven, 3001
Belgium

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