Abstract
The minimum covariance determinant (MCD) method is a robust estimator of multivariate location and scatter (Rousseeuw (1984)). Computing the exact MCD is very hard, so in practice one resorts to approximate algorithms. Most often the FASTMCD algorithm of Rousseeuw and Van Driessen (1999) is used. The FASTMCD algorithm is affine equivariant but not permutation invariant. Recently a deterministic algorithm, denoted as DetMCD, is developed which does not use random subsets and which is much faster (Hubert et al. (2010)). In this paper DetMCD is illustrated in a calibration framework. We focus on robust principal component regression and partial least squares regression, two very popular regression techniques for collinear data. We also apply DetMCD on data with missing elements after plugging it into the M-RPCR technique of Serneels and Verdonck (2009).
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References
BURNHAM, A.J., MACGREGOR, J.F. and VIVEROS, R. (1999): Latent variable multivariate regression modeling. Chemometrics and Intelligent Laboratory Systems 48(2), 167-180.
DE JONG, S. (1993): SIMPLS: an alternative approach to partial least squares regression. Chemometrics and Intelligent Laboratory Systems 18, 251-263.
HUBERT, M., ROUSSEEUW, P.J. and VANDEN BRANDEN, K. (2005): ROBPCA: a new approach to robust principal component analysis. Technometrics 47, 64-79.
HUBERT, M., ROUSSEEUW, P.J. and VERDONCK, T. (2010): A deterministic algorithm for the MCD. Submitted.
HUBERT, M. and VANDEN BRANDEN, K. (2003): Robust methods for partial least squares regression. Journal of Chemometrics 17, 537-549.
HUBERT, M. and VERBOVEN, S. (2003): A robust PCR method for high-dimensional regressors. Journal of Chemometrics 17, 438-452.
MARONNA, R.A. and ZAMAR, R.H. (2002): Robust estimates of location and dispersion for high-dimensional data sets. Technometrics 44, 307-317.
ROUSSEEUW, P.J. (1984): Least median of squares regression. Journal of the American Statistical Association 79, 871-880.
ROUSSEEUW, P.J. and CROUX, C. (1993): Alternatives to the median absolute deviation. Journal of the American Statistical Association 88, 1273-1283.
ROUSSEEUW, P.J., VAN AELST, S., VAN DRIESSEN, K. and AGULLO, J. (2004) Robust multivariate regression. Technometrics 46, 293-305.
ROUSSEEUW, P.J. and VAN DRIESSEN, K. (1999): A fast algorithm for the minimum covariance determinant estimator. Technometrics 41, 212-223.
SERNEELS, S. and VERDONCK, T. (2009): Principal component regression for data containing outliers and missing elements. Computational Statistics and Data Analysis 53(11), 3855-3863.
VERBOVEN, S. and HUBERT, M. (2005): LIBRA: a Matlab library for robust analysis. Chemometrics and Intelligent Laboratory Systems 75, 127-136.
VISURI, S., KOIVUNEN, V. and OJA, H. (2000): Sign and rank covariance matrices. Journal of Statistical Planning and Inference 91, 557-575.
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Verdonck, T., Hubert, M., Rousseeuw, P.J. (2010). DetMCD in a Calibration Framework. In: Lechevallier, Y., Saporta, G. (eds) Proceedings of COMPSTAT'2010. Physica-Verlag HD. https://doi.org/10.1007/978-3-7908-2604-3_61
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DOI: https://doi.org/10.1007/978-3-7908-2604-3_61
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